I honestly can't remember if there is any sort of warning before they're tired and ask to leave. I do know that at the start they can really only make it a handful of floors and by midway through they'll make it to the next boss floor with no issues. By the end of the game you'll easily go 20 floors or more without running out of stamina (of course the Tartarus blocks get a lot longer after the first two to make up for it). But honestly, I wouldn't worry too much about going every single night. Barring some event taking place that kept me from going for a bit I think I went every other day at most and got by just fine. I tried to make sure the main character was in great condition every time I went so I wouldn't get sick and lose valuable time recovering. And I found that was usually plenty. I had no real trouble finishing a block well before the full moon that way and never felt underleveled.

And there are a couple of social links that you can only access at night if I'm not mistaken so you're going to miss out on those if you go every night.