Per Raw, there is no answer. I would guess RaI that yes they can.
If a spell must be maintained with concentration,
that fact appears in its Duration entry, and the spell
specifies how long you can concentrate on it.
Page 203 PHB
You physically cannot concentrate on the spell any longer than that, which implies that there would be some form of magical stress as you came to the edge of your ability. It also make sense from game terms. The idea that invisibility simply lasts an hour, as if the caster set a magical timer seems at odds with the tone of the book and game which wants to keep some vaguery and mystery to magic and the game in general. It seems far more in keeping with theme for the wizard to be straining to keep it up and that's as long as he can manage, so he would know when it was about to fail.
We can ask why they wouldn't apply a formula based off of Con +Wis or something, or even a duration based on rolling. The likely answer is that wouldn't fit the more simplistic feel they were going for. Much like movement is done in feet but they want us to get rid of the grid based combat we can make that same assumption that time is in minutes but they want us to get rid of tracking per second and just go with a more general, it last approx this long.
It makes sense from a playing perspective as well. Is minute to minute tracking a feature of the game? How often does tracking the exact duration of a spell come up and how much extra book keeping will that do? Does that style of gaming fit the general action adventure theme they are pushing? Not so much. So while there could be alot of interesting RP elements with a wizard dropping his invisibility forgetting how long it lasted, it's far more likely to end with your party being way more conservative and only dong 45 minutes just to be sure nothing bad happens.