Knowing when you’ve had enough people for the day isn’t rude. It’s self-knowledge.

A limit on company is a fact about you rather than a judgement on anybody. The hours run out, and past that point you are present without being much use, which is worse company than a polite exit. Pretending the limit is not there produces the short tone and the blank stare at nine.

Say it plainly when you reach it, which is harder than slipping away but costs less. That you are done for today and it has nothing to do with them. People take that better than an evening of you being half there.