Answer

Night is not a time for tefillin. So in any case, nighttime is not relevant.
As for the question itself, I should preface that there is no clear source that one must put on tefillin every day. See the note in the article on Root 13 in the book He Shall Send Forth His Roots.
The situation you describe is what the later authorities (Acharonim) call “circumstances beyond one’s control on the last day” (see, for example, here). The term comes from the words of the Agudah regarding someone who postponed redeeming a house in a walled city until the last day of the twelve months and in the end forgot. Is he considered under compulsion, in which case he can still redeem it, or not? His conclusion is that he is not considered under compulsion (he derives this from Hillel’s enactment regarding houses in walled cities).
In contrast, the Ramah, cited in Nimukei Yosef on Bava Kamma, holds regarding the afternoon prayer that this does count as circumstances beyond one’s control (were it not for the fact that the Sages enacted in advance that a person should not sit with the barber close to the time of Mincha, which does not apply in our case).
However, Rabbi Chaim of Brisk, in the stencil notes, distinguishes between the cases and argues that there is no dispute. In any event, the situation you describe regarding tefillin is similar to the discussion about the afternoon prayer, and there it is considered circumstances beyond one’s control (because in our case there is no special enactment forbidding doing something before tefillin). So it seems to me that this is considered circumstances beyond one’s control.
But as stated, there is no practical difference, because in any case there is nothing you can do about it. There is no make-up, and it is not even certain that there is an obligation every single day.