It depends. Are they little things that he hasn't been given a chance to correct, or things that he's always done and you are now getting tired of it? If at the beginning he did these things and you accepted them, or you thought you could change him, then you might need to move on. If for instance it's things like he doesn't pick up after himself, or he doesn't like to hang out with your friends, that could possibly be modified with a heartfelt conversation. If it's that he hasn't ever worked, or he's disrespectful, then you might need to consider moving on.
You used the word unacceptable, that sounds like your mind is made up. You are either not open to negotiation, or your mind is telling you something your heart is not hearing.