Has any philosopher written approvingly of "living each day like it was your last"?
Or even, each thing you do (big or small) like it was the last thing you could?
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A biblical quote comes to mind: Matthew 6: 26 & 34
Look at the birds of the air; they do not sow or reap or store away in barns... do not worry about tomorrow, for tomorrow will worry about itself. Each day has enough trouble of its own.
Also sentiments of Buddhist non-striving (e.g. Cetana sutta). Basically, if you've got your life pattern sorted, ideally it shouldn't make any difference if today is your last day or not. So in a way, these ancient philosophies are in line with "living each day like it was your last".
If you focus on this as a principle and take it seriously, it minimizes the imperative to continue. For many people, if you can't look past your next action, and it is horrific, the only way to live as if it this were your last act is to make it your last act, and escape the horror.
Knowing you might be free of cancer next year does not help at all if you are seriously living each day as if it were your last, you should choose to skip chemotherapy and kill yourself when things get too bad. The imperative to live on for your children, or do what you can with your limited time left is excluded from consideration.
Neitsche escapes this trap by suggesting that you average this impulse out over your whole life, so the length of your life is part of the computation of its quality. This retains the wish to live so that the current moment is always infinitely important, while allowing you to look beyond it, and suffer now for future gain.
The common interpretation of the Eternal Recurrence is this idea expanded into a theory of life rather than of the moment. You are to live your life as if this is the last copy of your life in which you might possibly change anything, but there will be an eternity of copies to follow. So if you make this moment hell, that hell is eternally revisited, and if you make it blissful, you will relive that bliss.
Existentialism is another choice in this direction that avoids the trap. You have to take each moment and respond in good faith. That means that you cannot choose poorly and just accept that life is crappy. Disowning the responsibility is bad faith. So each moment needs to be considered in isolation, as well as in context. This might realistically be the last, or the only decision you get to make that is not determined for you. The odds of that may be low, but they are always there.
This directive to live not as though this moment were your last, but as if something eternally significant might happen at any moment, and you might have a part to play in that, is also a thread in Christianity, injected in consideration of Calvinism and its earlier deterministic echoes. It is put beautifully in some hymns, for instance "Once to Every Man and Nation" (https://www.hymnary.org/text/once_to_every_man_and_nation)