You are not giving up on her.I don't believe it to be right to just give up on someone.
You are giving up on you, one person in that relationship that does not deserve it.
A friend does not punch a friend because they feel like it. And while I can absolutely think of a thousand situations where a punch, alone, would not be abuse, or could be even helpful, yours does not sound like one.
She is not someone you need to worry about.