Isn’t the Tosefta I brought strong evidence? It really seems from there that the whole day is like a make-up period for the morning.

Indeed, that is how it seems there.

If we assume that tefillin are supposed to be worn only for a short time, then yes, that is indeed the meaning of the Tosefta.
But in truth, from the overwhelming majority of sources it clearly emerges that tefillin are supposed to be worn all day, and if so, the meaning of the Tosefta is that if he has not yet put them on in the morning and they are still not on him, he should put them on later, so that at least during the remaining time he will be with tefillin—and this is until evening, because tefillin are not worn at night (whether by Torah law or by rabbinic law is a dispute).
It’s like saying: put on socks in the morning, and if you didn’t, then put them on all day.

Here is the article (with the permission of Rabbi Yaavetz, may he live long and well):

Tefillin—As a Constant Memorial Before God

A. Four sections are in the tefillin.
B. Two foundations in the Exodus from Egypt.
C. The tefillin of the Master of the universe.
D. The combining of the sections as proof that the obligation of tefillin is for the whole day.
E. Days that are themselves a sign.
F. A source for putting them on at least once a day.
G. Tefillin as Torah study and in its place.
H. A new explanation of the story of Elisha of the Wings.
I. Summary

A. Four sections are in the tefillin.
There are four Torah passages that we were commanded to write in the tefillin. The deeper plain meaning of Scripture is that these are such basic foundations of faith in the thought and life of a Jewish person that the Torah warns that they must not depart from his mouth or his memory. For that purpose he must bind them on his hand and between his eyes, so that his whole life will be grounded on these principles. The tradition of our Sages, in accordance with a law given to Moses at Sinai, interpreted the commandment in its practical details—how to anchor these matters in actual deeds, just as a person does with matters important to him, writing them down and wearing them in prominent places.
There are four sections, four topics, four foundations of faith, without whose remembrance the Jewish person lacks the basis for the service of the Creator. The section of Shema establishes the foundation of God’s unity and love of Him, and in the language of the Mishnah (Berakhot 2:2), “acceptance of the yoke of the kingdom of heaven.” The section “And it shall be, if you indeed heed” establishes the doctrine of reward and punishment, that the Creator rewards those who perform His commandments and punishes those who transgress them, and in the language of the Mishnah there, “acceptance of the yoke of the commandments.” The sections “Sanctify to Me” and “And it shall be when the Lord brings you” recall the Exodus from Egypt.
So Nachmanides wrote (Exodus 13:16): “The root of this commandment is that we place the written account of the Exodus from Egypt on the arm and on the head, opposite the heart and the brain, which are the dwellings of thought. Thus we write the section ‘Sanctify’ and ‘And it shall be when the Lord brings you’ in the totafot because regarding this commandment we were commanded to make the Exodus from Egypt totafot between our eyes; and in the sections ‘Hear’ and ‘And it shall be if you indeed heed’ we were commanded likewise that we should make the commandments totafot, as it is written: ‘And these words that I command you today shall be upon your heart… and they shall be for totafot between your eyes.’ Therefore we write also those two sections as totafot, for they are the commandments of divine unity and remembrance of all the commandments and their punishment and reward, and the whole root of faith.” And more briefly, in the words of Sefer HaChinukh (commandment 422): “The idea in these four sections, more than in the other sections of the Torah, is that these contain acceptance of the yoke of the kingdom of heaven, the unity of God, and the matter of the Exodus from Egypt… and these are the foundations of the Jewish religion.” There are certainly additional foundations necessary for a Jew, and the Sages discussed whether to require additional sections to be inserted into tefillin—the section of tzitzit or the Ten Commandments (Sifrei Devarim, sec. 35)—but according to Jewish law only those explicitly stated in the Torah are written in tefillin. Thus the Torah determined that only these foundations are never to depart from before our eyes and opposite our heart.
But we began with four and ended with three. Why is there a need for two sections to remember the Exodus from Egypt? If the Torah commanded us to remember two sections dealing with the Exodus from Egypt, then necessarily there are two different foundations that require two sections. What is the additional foundation?

B. Two foundations in the Exodus from Egypt.
The Exodus from Egypt establishes faith in the Creator of the world and its Governor. He is the One who overturns the systems of nature, who speaks prophecy to His servants the prophets and sends them to created beings to warn and command them, and who judges the nations—and who can say to Him, “What are You doing?” Through the plagues of Egypt that brought Pharaoh to submission, God showed His great hand and outstretched arm so that we might recount His greatness in the ears of our children and our children’s children and plant faith in Him in our hearts. But an additional foundation is learned from the Exodus from Egypt, and it stands on its own. Taking a nation from within a nation teaches of God’s love for Israel, of the covenant with the fathers remembered for the children, so that we and the inhabitants of the world may know that God distinguishes between Egypt and Israel.
This important principle was emphasized throughout all the plagues, but especially in the plague of the firstborn. The main purpose of the plague of the firstborn, after all the other plagues, was the clarification and illumination of this principle. The disruption of nature in the plague of hail, for example, is more striking and resounding than in the plague of the firstborn, and indeed with hail the Torah emphasizes more the knowledge of the Holy One’s power (Exodus 9:16): “But indeed for this reason I have kept you standing: in order to show you My power, and in order that My name be told throughout all the earth.” The plague of the firstborn has great force in proving the distinction between Egypt and Israel, which indeed existed in other plagues as well, but here it seems that this is its central point (11:7): “So that you may know that the Lord distinguishes between Egypt and Israel.”
At Mount Sinai God opened and said (20:2): “I am the Lord your God, who brought you out of the land of Egypt, out of the house of bondage.” Throughout the Torah, the reason for accepting the yoke of the commandments because of the Exodus from Egypt appears many times. This reason divides into two: God’s greatness obligates accepting the yoke of His kingship, and gratitude for our salvation leads to the making of the covenant. In the language of prayer one might say: Our Father, our King. “Our Father” is a relation of closeness, because He brought us forth as a nation from within a nation; and “our King” is a relation of servants, for God is in heaven and we are on earth. Whether as children or as servants—in love and in awe.
The two sections in tefillin, “Sanctify” and “And it shall be when the Lord brings you,” separately bring these two foundations to remembrance, on the basis of the Exodus from Egypt. The section “Sanctify” indeed opens with the command to sanctify the firstborn, but without giving a reason. Moses’ words to the people deal with remembering the day of the Exodus and the service of Passover, and the telling to the son concerns the Exodus from Egypt itself, which obligates these commandments. That obligation is toward our King, from awe, because of His greatness and might.
The section “And it shall be when the Lord brings you” emphasizes the distinction of Israel. The sanctification of the firstborn, redemption of the human firstborn, sacrifice of the firstborn of a kosher animal, and the commandment of the firstborn donkey all sharpen the plague of the firstborn as distinct from the other plagues of Egypt, and establish the yoke of the commandments on the foundation of gratitude (13:15): “And the Lord killed every firstborn in the land of Egypt… therefore I sacrifice to the Lord every male that opens the womb, and every firstborn of my sons I redeem.” This section establishes the principle of love for our Father, because of His choosing our fathers and us.

C. The tefillin of the Master of the universe.
It may be possible to find support for this division between the section “Sanctify” and the section “And it shall be when the Lord brings you” in the words of the Talmud (Berakhot 6a), which details the four sections in the tefillin of the Master of the universe: “Rav Nachman bar Yitzchak said to Rav Chiyya bar Avin: In these tefillin of the Master of the universe, what is written in them? He said to him: ‘Who is like Your people Israel, one nation in the land’… The Holy One, blessed be He, said to Israel: You have made Me a unique unit in the world, and I will make you a unique unit in the world. You have made Me a unique unit in the world, as it is said: ‘Hear, O Israel, the Lord our God, the Lord is One’; and I will make you a unique unit in the world, as it is said: ‘Who is like Your people Israel, one nation in the land.’ Rav Acha son of Rava said to Rav Ashi: That works for one compartment; what about the other compartments?… Rather: ‘For what great nation is there…’ and ‘And what great nation is there…,’ which are similar to each other, in one compartment; ‘Happy are you, O Israel’ and ‘Who is like Your people Israel’ in one compartment; ‘Or has any god attempted to come and take for himself a nation from within a nation’ in one compartment; ‘And to make you supreme’ in one compartment.”
The first section the Talmud parallels to the section of Shema. The Holy One singles out Israel just as Israel singles out Him. It seems there is a parallel also between the other themes and the sections in tefillin, according to what we said above: “Who is like Your people Israel” and “Happy are you, O Israel” (Israel’s uniqueness by God and His love for them) parallel Shema; “And to make you supreme” (as reward for observing the Torah, Deuteronomy 26:16–19) parallels “And it shall be if you indeed heed”; “For what great nation is there” and “And what great nation is there” (Israel’s greatness) parallel the Exodus from Egypt in the section “Sanctify”; “Or has any god attempted to come and take for himself a nation from within a nation” (God’s choosing of Israel) parallels the plague of the firstborn in the section “And it shall be when the Lord brings you.” Here too there is a similarity, conceptual and linguistic, between the third section and the fourth, except that one magnifies Israel and one emphasizes the choosing of Israel from Egypt, just as in our tefillin one magnifies the Creator (“Sanctify”) and one deals with God’s choosing of Israel (“And it shall be when the Lord brings you”).

D. The combining of the sections as proof that the obligation of tefillin is for the whole day.
This remembrance, whose plain meaning is that it not depart from our heart and not leave from before our eyes—does its fulfillment take place once a day or at all times? Seemingly, the commandment of tefillin applies all day, for the Torah gave them no fixed measure or limit, except only times that were excluded—night and Sabbaths and holidays according to some tannaim (Eruvin 96a and elsewhere). On the other hand, the common reality is that the commandment of tefillin is fulfilled only for a small part of the day.
Many sources simply indicate that their main commandment is to be worn all day; only because of the difficulty of preserving their holiness was their actual wearing limited to the time of Shema and prayer, so that at the very least one should not be like one who bears false testimony when he says the verses commanding tefillin and does not fulfill them. The proofs in both directions are well known, but it should be argued that even the familiar external structure of tefillin itself clearly proves that their main commandment is for the whole day, for otherwise tefillin would not look the way they do.
The Torah commanded in four different passages to bind them on the arm and between the eyes, and in each section the command appears in that section itself, with no verse connecting these commands. The Talmud says (Menachot 44a) that one who puts on tefillin fulfills eight positive commandments—four on the arm and four on the head. But in the enumeration of commandments only two were counted, one for the arm and one for the head, because the four sections are interdependent, as Maimonides explained in the eleventh root. From where do we know that there is any practical connection between them? Why should we not put on four separate tefillin, each containing one section? What is the source for joining all the remembrances together? After all, there are four completely separate commands in the Torah.
The baraita (Menachot 34b) expounds: “The Sages taught: One might think he should write them on four parchments and place them in four compartments on four parchments. Scripture says, ‘and for a memorial between your eyes’—I told you one memorial, not two or three memorials. How so? He writes them on four parchments and places them in four compartments.” (Later there it is explained that this refers to the head-tefillin, while for the hand-tefillin it is one parchment in one compartment.) The baraita is essentially asking our question: from where do we know there is a connection between the different remembrances? Why should we not wear four tefillin with four sections on the arm, and similarly on the head, with no connection between them? The baraita’s answer is that there is no place for several remembrances. But this answer is hard to understand. Can one derive that we should not eat matzah and bitter herbs one after the other, or the festival offering and the Passover offering, because there are two eatings here? Can one derive that there should not be room for two recitations in one day, for example Shema and Grace after Meals? Surely it is clear that one can do one act after another with no contradiction between them. How does wearing several different tefillin contradict the fact that each remembrance stands on its own?
Clearly, the intention of the exposition is that one cannot place several remembrances on the same place on the body, since the place of tefillin is identical for all the sections. Even if physically there is room on the head to place two tefillin, and if they were smaller—each containing only one section—perhaps there would be room even for four tefillin, still the exposition is that one should not remember more than one thing separately; rather, they must be unified into one combined remembrance. But this exposition makes sense only if all the remembrances are worn at the same time. If the Torah’s intent were that they be worn once a day, one could put them on one after another, just like all commandments that a person fulfills one and then the other, even on the same limb, and there would be no conflict at all. So it is clear from the exposition that remembrance is something fixed constantly in its place; it is impossible to explain the Torah as meaning to remember each section during a different part of the day, for then not even one of the remembrances would be fulfilled in full. If the Torah commanded remembering four matters, and the wording of the Torah indicates that there are not to be “two or three remembrances,” then the only way is to unify all the remembrances and wear them attached together, since all of them must be worn at one time.
In short, we may say this as follows: if the commandment of tefillin were time-limited like the doing of an act, then one could do several acts one after another and there would be no contradiction at all to the Torah’s language. Only if the wearing of tefillin is an ongoing state would several tefillin at the same time parallel several remembrances—and that is not what the Torah’s language implies. It follows that the form of tefillin proves that tefillin accompany the Jew throughout all his time, insofar as possible.

E. Days that are themselves a sign.
In a baraita (Menachot 36b and Eruvin 96a) it says: “Rabbi Akiva says: One might think a person should wear tefillin on Sabbaths and holidays; Scripture says, ‘and it shall be for a sign upon your hand and for frontlets between your eyes’—those that need a sign, excluding Sabbaths and holidays, which are themselves a sign.” Rashi explains (Eruvin there, and briefly in Menachot there): “Those that need a sign—days when Israel need to establish a sign upon themselves to show that they hold fast to the Torah of the Holy One, blessed be He. Excluding Sabbaths and holidays, which are themselves a sign between the Holy One and Israel, as it is written (Exodus 31:13), ‘for it is a sign between Me and you.’” Tosafot (Menachot there, s.v. “excluding”) and those who follow them maintain that not only the prohibition of labor constitutes a sign, but also eating matzah throughout the days of Passover and dwelling in the sukkah throughout the festival are likewise a sign. And in Eruvin (96a s.v. “days”) they wrote that the prohibition of labor on Chol HaMoed is the sign, and therefore Chol HaMoed is exempt from tefillin. Many medieval authorities (Rishonim) disagree; see below in section F.
On the face of it, Tosafot’s position is difficult. Regarding Sabbath it says, “for it is a sign,” as Rashi explained, and a holiday may be compared to Sabbath. Even the prohibition of labor on Chol HaMoed can be said to be an extension of the prohibition of labor on a holiday and thus similar to it. But why should the performance of commandments on Chol HaMoed be considered a sign that exempts one from tefillin, as Tosafot hold in Menachot? Especially eating matzah during the days of Passover, which is optional, unlike sukkah where if one wants to eat he is obligated to eat in the sukkah, and if he eats outside the sukkah he neglects a positive commandment. On Passover there is no neglect of a commandment, and plainly even fulfillment of a commandment is not so simple to say. True, the Vilna Gaon’s view that there is a commandment in this is well known, but it still requires examination: does every commandment exempt one from tefillin?
This should be understood in light of what we wrote in section A above and in note 1: the deeper intention of the Torah is to remember matters of faith at all times, and that they not depart from our heart and our eyes. Actually putting on tefillin is the “sign,” meaning a remembrance so that we not forget this. About this Rabbi Akiva expounded, “Those that need a sign, excluding Sabbaths and holidays, which are themselves a sign.” That is, on the Sabbath a person cannot remove faith in divine unity from his heart, since the entire cessation of the day reminds him of it, and likewise on holidays. To this Tosafot added that the festivals too do not need a sign, for a person remembers on them the Exodus from Egypt and faith in divine unity at every hour through his food and his dwelling. Even acts that are not actually the fulfillment of a commandment remind one of faith by the very change from routine. These are not “days when Israel need to establish a sign upon themselves to show that they hold fast to the Torah of the Holy One,” in Rashi’s words above.
It should be added that Scripture explicitly states that the practices of those days are meant to remind us of the Exodus from Egypt for the entire rest of the year. Of matzah it says: “You shall not eat leaven with it; seven days you shall eat with it unleavened bread, the bread of affliction, for in haste you came out of the land of Egypt, so that you may remember the day when you came out of the land of Egypt all the days of your life” (Deuteronomy 16:3). The plain meaning is that the purpose of eating matzah seven days a year is that this should suffice to remember it all year. Likewise regarding the commandment of sukkah it says: “So that your generations may know that I caused the children of Israel to dwell in booths when I brought them out of the land of Egypt” (Leviticus 23:43). Here too it is explained that the purpose of dwelling in the sukkah during those seven days is to remind forever, for generations. If so, there is indeed no need during them for a sign to remember faith and service of God. Only on ordinary days, when one is not occupied with this remembrance all day, is there a need for a fixed sign to remind him.
This understanding also sharpens what was said above, that the need for the sign is not for one moment in the day but as an ongoing state. For if the need were only once a day, then at the time one is performing a commandment, such as reciting Shema, certainly “he himself is a sign,” and this would be no less than eating matzah or dwelling in the sukkah. At that moment he does not need to establish a sign on himself to show that he holds fast to God’s Torah, in Rashi’s words above. So why would tefillin be needed?
Rather, on festival days acts of faith accompany the day over its course, and even if not continuously in the literal sense, they are nonetheless present throughout the hours of the day (and indeed Tosafot mentioned the commandment of sukkah and not the commandment of lulav, since “as soon as he lifts it he has fulfilled it”). But on ordinary days there is no such commandment, and therefore the Torah required tefillin as a fixed sign—even though one is not actually obligated to wear them literally all day, as will be discussed below in section G.

F. A source for putting them on at least once a day.
According to what we have said, this commandment has no upper limit in terms of time. Does it have a lower limit? Is there a minimum time of wearing by which one fulfills his obligation, such that less than that is considered neglect of a positive commandment? The accepted view is that once a day is the minimum, and one who passes a day without putting on tefillin has neglected a positive commandment. The insistence on putting them on once a day at the time of reciting Shema and the morning prayer comes from the words of the Sages: “as though he bears false testimony.” But seemingly this is not a law from the laws of tefillin, but rather to avoid false testimony (in practice this is guidance as to when to wear tefillin, and so of course it appears in the laws of tefillin). If a person was prevented and recited Shema without tefillin, why must he specifically put them on that same day? In the words of the Sages we have not found a source for this measure.
As brought above, according to Tosafot Chol HaMoed is exempt from tefillin. By contrast, the Rosh and those who follow him hold that Chol HaMoed is obligated in tefillin. The decisors discussed this at length (see Beit Yosef, sec. 31), and as is known, the Shulchan Arukh ruled (sec. 31:2) to exempt, mainly because of the Zohar cited by the Beit Yosef, whereas the Rema brought the Ashkenazic custom to wear them with a blessing. There are also those who had the custom to wear them without a blessing or privately, and this is longstanding. Seemingly, if the obligation to wear tefillin is once a day as a matter of strict law, how did the Jewish people adopt a lenient practice regarding a doubtful Torah positive commandment, without the law having been clearly decided? Were the views of one camp of medieval authorities (Rishonim) really set aside leniently because of another camp of medieval authorities and the warning of the Zohar, to the point that there was no concern at all for neglecting a positive commandment? That does not seem to be the normal way Jewish law is decided. It appears from this that neglecting one day is not considered neglect of a positive commandment; rather, this measure is a Jewish custom so that the commandment of tefillin not be entirely lost.
In tractate Shevuot (25a) there is a dispute regarding an oath of utterance about the past, where no such oath is possible about the future—for example, one who swears that so-and-so threw a pebble into the sea, where one cannot swear that he will throw it, since this is not in the power of the one swearing—whether he brings a sliding-scale offering. Rav obligates and Shmuel exempts. Rav Hamnuna challenges Shmuel (25b) from the Mishnah at the end of the chapter (29b): “ ‘I did not eat today’ and ‘I did not put on tefillin today’—if one says, ‘I adjure you,’ and he answered Amen, he is liable. Granted, ‘I did not eat’ exists in the future form ‘I will not eat’; but ‘I did not put on’—does it exist in the form ‘I will not put on’?” Rashi explains: “Does ‘I will not put on’ exist—as an oath of utterance? But this is one who swears to nullify a commandment.” Rav Hamnuna answers that according to Shmuel the Mishnah means liability to lashes if done intentionally, although if done unintentionally he is exempt from an offering. Seemingly the opposite of “I did not put on tefillin today” is “I will not put on tefillin today,” and Rav Hamnuna challenged that such an oath does not take effect because one is swearing to nullify a commandment. Is this a source that specifically neglecting tefillin for an entire day counts as neglecting a positive commandment? Or perhaps even if one swears not to put them on for half a day, that counts as swearing to nullify a commandment and the oath does not take effect? Seemingly one cannot say that, for the vast majority of people do not wear tefillin all day, and we do not consider this neglect of a positive commandment. How can it be that one who swears not to do what in any case he is not doing is considered to have sworn to nullify a commandment, while the person himself is not considered to be neglecting a commandment? One might say that any act whose performance is a commandment cannot be nullified by oath, even though the commandment could be fulfilled in another way. So even though not wearing tefillin at every moment is not actual neglect of a commandment, since wearing them for additional time is fulfillment of a commandment, an oath to nullify that commandment does not take effect.
However, the Mishnah above (21a) gives an example of an oath of utterance for which one is liable: “He said, ‘I swear I will give to so-and-so, and I swear I will not give.’” The Talmud asks: “What is ‘I will give’? If you say charity to a poor person—he is already sworn from Mount Sinai, as it is said (Deuteronomy 15:10): ‘You shall surely give to him.’ Rather, it means a gift to a rich person.” Rashba wrote (s.v. “if you say,” and see also Ritva and Meiri): “Some of our great French teachers of blessed memory said that this is specifically when a poor person asks him for charity, for then he is obligated to give him; but regarding a poor person in general, the oath takes effect, because he is not obligated to go and support poor people constantly. It also seems to me that this is specifically for a small gift sufficient for temporary sustenance, as they said (Bava Batra 9a), ‘he gives him sustenance for the night’; but beyond this he is liable, because he is not sworn to make him rich.” Thus only if not doing the act is actual neglect of a commandment—such as when a poor person stands before him and he is obligated to give him at least enough for a night’s sustenance—does the oath not take effect. But if he swore not to give more than the minimum obligation, the oath takes effect, even though certainly if he gives more he fulfills a commandment. The Machaneh Ephraim (Shevuot sec. 15) discusses whether an oath not to give charity to a particular poor person takes effect, since he can give charity to another poor person and others can support this one, so that this is not neglect of a commandment. He cites Rashba’s words and challenges him, because from the Talmud (Kiddushin 8b and Nedarim 65b) it is clear that a poor person is not cast upon one specific person to support, and a person may say that someone else should support him. From Maimonides’ wording he inferred that only if one swore not to give any charity at all to poor people does the oath not take effect. It is explained from this that for an act of commandment whose omission is not full-fledged neglect of a commandment, an oath does take effect. If so, regarding an oath not to put on tefillin, only when not putting them on is total neglect does the oath not take effect. One might distinguish, however, that if he does not give charity to this poor person but gives to another poor person, the commandment has been fulfilled equally; but if he did not put on tefillin for some time from within a desire to neglect the commandment, there is no way to make up the commandment at another time, because that would be a different obligation.
Maimonides wrote (Laws of Oaths 5:14–16): “Likewise, anyone who swears to nullify the commandment and did not nullify it is exempt from an oath of utterance and is lashed because of a false oath, and he performs the commandment he swore to nullify. How so? For example, if he swore not to make a sukkah, not to wear tefillin, and not to give charity… If he swore to fulfill a commandment and did not fulfill it, he is exempt because of an oath of utterance. How so? For example, if he swore that he would perform lulav or sukkah or give charity to a poor person… for an oath of utterance applies only to optional matters, where if he wishes he does and if he does not wish he does not do, as it says, ‘to do harm or to do good.’” Regarding nullifying a commandment he wrote “not to wear tefillin” and gave no time measure; whereas regarding fulfilling a commandment he did not give tefillin as an example.
Perhaps it should be explained that in fulfilling a commandment, since indeed there is no total obligation to wear them at every moment (and see further below), the oath takes effect, because he adds a total obligation that did not exist before the oath. But in nullifying a commandment, the oath does not take effect concerning an act whose omission is neglect of a commandment, even if it is not complete neglect, as we suggested above. Or perhaps Maimonides means not to wear tefillin ever, and neglect from that point onward is neglect of a commandment; whereas an oath to wear tefillin cannot be interpreted as obligating wearing them at every moment, but he can add in his wearing of them, and it cannot be said that the oath concerns only what he was already obligated in anyway. This still requires examination.
But I found in the Jerusalem Talmud (Horayot 1:3) a source that seemingly indicates a measure of at least once a day: “A prophet and an enticer—might it be that if they tell you, ‘Do not put on tefillin today; put them on tomorrow,’ you should listen to them? Scripture says, ‘to walk in them’—in all of them, not in part of them; thus you have uprooted the Name for that entire day.” The baraita expounds that only if a false prophet and enticer ask one to violate an entire commandment are they liable to death, and as an example it gives the cancellation of one day of tefillin. This implies that each day is a commandment unto itself and neglecting one day counts as neglecting a commandment. Perhaps, however, according to the opinion that night is not a time for tefillin, there is reasoning that each day renews a separate obligation; but according to the opinion that night is a time for tefillin, the obligation is continuous and a separate day has no significance. (And even the rabbinic prohibition against wearing them is only from concern lest one sleep in them, and it does not essentially interrupt the obligation; therefore there is also no reason that there should be a new rabbinic obligation each day.)

G. Tefillin as Torah study and in its place.
The halakhic definition of the commandment of tefillin requires clarification. The commandment of tzitzit, for example, applies whenever a person wears a garment that is obligated, and one who removes his garment must make the blessing again when putting it back on if there was an interruption, because he is again fulfilling a complete commandment. By contrast, the commandment of lulav, for example, is fulfilled once a day, and although the people of Jerusalem would carry the lulav all day out of love for the commandment (Sukkah 41b), and there is also a commandment to wave it during Hallel, which has the status of an adjunct to the commandment (ibid. 37b), nevertheless once he has fulfilled his obligation he may no longer make another blessing (ibid. 46a; Shulchan Arukh 651:5, Rema). The definition of tefillin lies between these two. On the one hand, one who puts them on, removes them, and diverts his attention, then puts them on again, returns and makes the blessing, because he is fulfilling a complete commandment. But on the other hand, one who does not put them on again is not neglecting a positive commandment like one who walks in a garment without tzitzit, and the vast majority of people go most of the day without tefillin. What is this intermediate definition?
The commandment of Torah study has a similar definition. On the one hand, its neglect occurs only when one passes an entire day without studying Torah, and once a person has recited Shema he has fulfilled “it shall not depart” (Menachot 99b). On the other hand, every time he studies Torah he fulfills a complete commandment, and if he diverted his attention he would need to make the blessing again several times a day—except that usually it is not considered diversion of attention. The definition of Torah study is that a person should study during all his free time, when he is not occupied with bodily needs and ordinary livelihood and is not engaged in a time-sensitive commandment. Perhaps the same is true of tefillin. Their commandment is to wear them whenever one is fit and able to do so. One who refrains because of his needs, because his body is not in a fitting state, and the like, bears no sin. But one who neglects them for no valid reason is acting improperly. Even so, one may not pass an entire day without them, as stated above (and in this too they resemble Torah study).
This similarity between Torah and tefillin is indeed brought in the Talmud in several contexts. In Kiddushin (34a): “Women are exempt from positive time-bound commandments. From where do we know this? It is learned from tefillin: just as women are exempt from tefillin, so too from all positive time-bound commandments women are exempt. And tefillin itself is learned from Torah study: just as women are exempt from Torah study, so too women are exempt from tefillin.” And we find (Sukkah 28a) praise of Rabban Yoḥanan ben Zakkai and Rabbi Eliezer that they did not walk four cubits without Torah and without tefillin—both together.
At the end of tractate Tefillin it says: “Rabbi Eliezer used to say: Great is the commandment of tefillin, for thus the Holy One said to Israel: ‘You shall meditate in it day and night.’ Israel said before the Holy One: Master of the universe! Are we able to meditate day and night? The Holy One said to them: My children! Put tefillin on your heads and on your arms, and I will regard it for you as though you are meditating on Torah day and night, as it says: ‘And it shall be for you as a sign on your hand and as a memorial between your eyes, so that the Torah of the Lord may be in your mouth.’” More than this, we find in the Mekhilta—and it was ruled in Jewish law in the Tur and Shulchan Arukh (38:10)—that one who is engaged in Torah study is exempt from tefillin. The medieval authorities (Rishonim) disagreed over the meaning of this ruling, and later decisors qualified the exemption; see all that there in the commentaries.
It seems that the definition of the commandment of tefillin is that Torah study should be realized either in speech or in action, and at least in one of them. Binding the main principles of Torah upon the heart and between the eyes parallels Torah study and meditation and completes them, especially at a time when we cannot engage in study properly. Thus one who is engaged in Torah study does not need this. It is specifically in his business and his walking about that the reminder is more important. Yet if he holds onto this and does not let go of that either, then his reward is with him and his recompense before him, as with the greatness of Rabban Yoḥanan ben Zakkai and Rabbi Eliezer who were careful to hold both together. Likewise we find (Bava Kamma 17a) that Rabbi Yoḥanan did not answer his student’s question when he came out of the bathroom until he had put on tefillin. According to the version in the She’iltot (cited there in Tosafot s.v. “but did he not say”), Torah is the study and tefillin are the practice, and in the study of an individual it is preferable to give precedence to Torah over tefillin because study is greater than action.
In addition, priests during their Temple service are exempt from tefillin (though they may wear the head-tefillin but not the hand-tefillin because of interposition, Zevachim 19a; Maimonides, Tefillin 4:13; Temple Vessels 10:6). It follows that one who is occupied in divine service in action—the sacrificial service—or in thought—Torah study—is exempt from tefillin. Tefillin are meant primarily to complete the absence of the ability to engage in the service of God in practice at every moment, and through tefillin one will not divert his attention from the service of God. (The remembrance of tzitzit has a different definition: like a servant marking on his garment his obligation to his master, and like a prince marking on his garment his closeness to royalty; this is not the place to elaborate.)
And I saw a precious idea: that the Torah defined tefillin as an ornament; see above note 3. A person ordinarily adorns himself with his ornaments on a regular basis, but removes them in the course of ordinary life. So too one should fulfill the commandment of tefillin: if a person removes them because of some reason or distraction, and even in the course of ordinary routine from time to time, that is not neglect of a commandment. But if a person no longer sees them as an ornament fit to be worn beyond the bare minimum obligation, it may be said that he has lost the Torah’s intent.
In actual practice, the vast majority of people do not wear tefillin all day, and from this developed the care not to engage in idle conversation while wearing them—even permissible ordinary talk. One who wears them all day certainly conducts with them permitted and appropriate worldly matters, such as business and labor and the like, and as stated, this is the Torah’s intent: that he sanctify through them all his ways of life. However, one who wears them only during prayer is careful to remove them before doing any act not part of the prayer, and thus the feeling took hold that even permitted speech that is not words of Torah and prayer somehow detracts from the holiness of tefillin, and that a person should remain in a kind of speech-fast while they are upon him.

H. A new explanation of the story of Elisha of the Wings.
In earlier times too, even daily wearing of tefillin was not always self-evident. This emerges from Tosafot (Shabbat 49a s.v. “like Elisha”), and the testimony of the SeMaG (positive commandment 3) is well known—that he made great efforts to restore the commandment of wearing tefillin to the Jewish communities after seeing that the commandment had been neglected.
Already in the Talmud (there 130a) it says: “It was taught: Rabbi Shimon ben Elazar says: Every commandment for which Israel gave themselves over to death at the time of persecution, such as idolatry and circumcision, is still firmly held in their hands. But every commandment for which Israel did not give themselves over to death at the time of persecution, such as tefillin, is still weak in their hands. For Rabbi Yannai said: Tefillin require a clean body like Elisha of the Wings. What is that? Abaye said: that one not pass gas while wearing them. Rava said: that one not sleep in them. And why did they call him Elisha of the Wings? Because once the wicked kingdom decreed persecution upon Israel, that anyone who put tefillin on his head would have his skull pierced, and Elisha would put on tefillin and go out to the marketplace. An officer saw him. He ran away from him and the officer ran after him. When he reached him, Elisha removed them from his head and held them in his hand. He said to him: What is in your hand? He said to him: Dove’s wings. He opened his hand, and indeed there were dove’s wings in it. Therefore they called him ‘Master of Wings.’” (The story is also brought in Shabbat 49a.)
This story and the law learned from it raise two difficulties. First, from where do we know that Elisha maintained a clean body? Tosafot (49a s.v. “like Elisha”) explained that had he not preserved the holiness of tefillin with a clean body, a miracle would not have been done for him. But this is very difficult: if there is no law requiring one to keep a clean body, why should a miracle not be performed for him? And if the point is that even without a binding law, clearly there is a pious practice to keep a clean body, how can one prove from here that this is indeed a full obligation? Perhaps Elisha acted piously, and therefore a miracle was done for him.
A second difficulty raised by the medieval authorities (Rishonim): how was Elisha permitted to remove the tefillin when the officer reached him? At a time of persecution one must give up his life for any commandment, even for a shoelace. Several answers were given by the medieval authorities (Rishonim). Tosafot (there s.v. “he removed them”) answered that many Jews go without tefillin, and this does not appear like nullifying a commandment, nor even like a gentile practice. Ran in his novellae and Nimukei Yosef in Sanhedrin (17b in Rif pagination) answered that the gentile could remove them from his head by force anyway, and this is like passive ground, where there is no obligation of martyrdom, because the act will be done either way.
The story can be explained differently, and the two difficulties are resolved through each other. Elisha in fact did not remove the tefillin despite the danger, because at a time of persecution one must give up his life for any commandment. However, once the officer reached him, Elisha feared that because of the terror of death he would be unable to maintain a clean body, and so he removed the tefillin from his head to preserve their holiness, not in order to save himself. Once he had already shown his refusal to submit to the officer by not removing them earlier, there was no concern that it would look as though he was yielding to the decree.

I. Summary:
There are four sections in tefillin: the unity of God and love of Him, belief in reward and punishment, strengthening faith through the Exodus from Egypt, and the choosing of the Jewish people through the plague of the firstborn. In the tefillin of the Master of the universe there appear four similar principles regarding the Jewish people.
The joining of the four principles into one commandment of tefillin comes from the obligation to remember these principles all day, and therefore there is no room for several remembrances simultaneously in parallel; rather, they must be unified into one remembrance. If it were correct from the outset to suffice with remembrance during only part of the day, one could divide the time among the four remembrances. At the same time, there is a minimum measure of once a day. The definition of the commandment resembles Torah study, which should be fulfilled as much as possible, but at least once a day. Tefillin are Torah study in action, and their main purpose is to save one who does not study Torah from diverting his attention from the service of God.
At the time of the decrees, Israel did not give themselves over for this commandment, and it therefore remains weak in their hands—except for Elisha, who gave himself over for their fulfillment and removed them only because of their holiness, not out of fear of death.

Thanks (though the article is already on the HaOtzar site, like all the other issues). In my humble opinion, the Jerusalem Talmud says exactly the opposite. It asked regarding forbidden fats about uprooting part of the commandment (the question isn’t so clear, but from what follows you can understand it). It brings a baraita that asks whether, if the prophet uproots one day of tefillin, should we listen or not? Scripture says, “to walk in them,” and not in part of them. Meaning: uprooting one day is not considered uprooting the entire commandment, and therefore we uproot that day. (And according to your explanation, why would the baraita even need to mention “and not in part of them”? It’s irrelevant.) Then the Jerusalem Talmud objects: “But you have uprooted that entire day!” And it answers that there is no uprooting of the body of the commandment here, and therefore we listen to the prophet and do not put them on that day. And that also answers the question about the fats. After that it brings that another amora asked the same question about carrying from one domain to another: if we permitted carrying one cubit in the public domain and not two, why is that not considered uprooting? after all we uprooted that entire cubit! And it answers similarly.

A. Regarding the Jerusalem Talmud: obviously uprooting one day is not uprooting an entire commandment, since yesterday he put them on and tomorrow he will put them on. Rather, the Jerusalem Talmud is discussing whether uprooting one instance of fulfilling the commandment counts as uprooting. That is the connection to “and not in part of them,” since the plain meaning of the passage deals with a prophet and an enticer who say to cancel one commandment entirely and remove it from the Torah.

B. The article is indeed in HaOtzar, and it also has the many footnotes on the body of the article there. But here, on the other hand, there are a few additions written after its publication in HaOtzar. One of them is the discussion in tractate Shevuot, where there may also be a source for once a day.

C. Regarding the Tosefta with which you opened and to which I responded: yes, it still requires examination. I agree that your interpretation is the straightforward one in the language of the Tosefta, in line with our present-day practice of putting them on for a limited time once a day, and the discussion is whether that has to be specifically in the morning. But it seems to me that it is very hard to interpret it that way in an early tannaitic source, and as I wrote, the commandment of tefillin is not for a limited time but for all the time. True, we are now discussing what the minimum is, but in any case that does not emerge from the language of the Tosefta, because there would be no need to say that if he did not put them on in the morning he should put them on all day, since even if he did put them on in the morning there is no reason he should remove them before the end of the day. The Tosefta should have said: From when is their time? In the morning, and all day is their time.

One may also wonder about the order of the halakhah there, which lists several commandments and spells out their blessings, and specifically with tefillin suddenly starts discussing their timing. Why? Is there perhaps an addition here? It needs to be checked in Tosefta Kifshutah.

I just checked Tosefta Kifshutah here

Click to access liberman_tosseftazraim1.pdf

He suggests that the discussion in the Tosefta is not when to put them on, but when to recite the blessing, based on Sukkah 46.

Seemingly, the Tosefta’s statement can be explained as a tradition not far from Ulla’s statement: that ideally one should put on tefillin in the morning, in line with the familiar tradition:
Rabbi Chiyya in the name of Rabbi Yoḥanan: What is the reason they said that a person puts on tefillin, recites Shema, and prays? So that he may accept upon himself the kingdom of heaven in complete form.

And if he did not put them on in the morning, he can still put them on all day.

Precisely from the sources at the beginning, it seems that tefillin should be worn all day.
The wording is quite clear.
Not vague.