I wouldn't so much call it "giving up"... to me as long as there is forward momentum towards working an issue out, then I can be patient, compassionate and really quite helpful. If someone absolutely refuses to admit an issue or a problem, and/or refuses to work on the issue or problem I will leave. I don't see that as giving up, it's more just the consequence of a choice the other person made.
I had to make that decision in a past relationship, and I do not regret it one bit.