TL;DR Play until you're not having fun anymore, and then play an extra 10 minutes. It might be uncomfortable, but you won't hurt yourself. Happy practicing!

Bottom lip pain isn't fun, but I usually don't feel the need to stop playing until a while after I start tasting blood (this doesn't mean I'm actually bleeding, my lower lip just starts to get a bit of that metallic-blood taste to it). When I play for long enough to get that taste, that's a good sign my lip will be sore in the morning. I would avoid getting to that point if you need to play for extended periods for the next few days, but that's because it's not fun, to the best of my knowledge a sore lip will almost never cause long lasting problems.

I have two signals that I really need to stop playing: the first is when my cheek muscles start failing and I can't keep a tight embouchure. Sometimes I push through that, although the quality of my playing diminishes significantly. A little after that starts, whatever muscle that regulates airflow between the nose and the mouth stops working properly. Air starts to leak out of my nose as I play, and everything just feels wrong. That is when I know I really need to put away the saxophone.

For some personal background: I'm a semi-serious amateur player who spends a good amount of time playing on the street corner. That is to say, I can play alright, but I also don't really know what I'm talking about. There's plenty of good advice about "not biting," and other things, but those are all easier said than done, and come with years of practice and playing (while being made aware of the correct ways of doing things. As an old band teach of mine once said, "Practice doesn't make perfect, perfect practice makes perfect!") But I figured as a regular street musician, I could give some decent advice about when playing just stops being worth it.