Once, yes. Twice, maybe. Thrid time -- no.

That depends on who is apologizing to whom and for what sort of behaviour?

That depends on if the apology was for something that happened in the past and there was no promise of it not happening again. The apology and the promise not to re-offend are 2 different things. In my experience, If you keep allowing the offending behavior to continue, without consequence, that gives permission to continue offending.

If the behavior doesn't change immediately, it doesn't necessarily invalidate the apology. But if they continue again and again and again to do the thing they apologized for, I would eventually take it as an indication that the apology was not sincere.

I'd have to say no.