At what point do you give up on a relationship?

Please be more specific. What problems are you dealing/fighting with?

When one of you becomes unwilling to work with the other to solve your problems through honest communications to reach a decision that benefits you both.

As long as your both willing to keep working, there is always hope.

If either partner chooses to stop fighting for the relationship or if it's always a 'fight', the relationship is already over.

The funny thing with love is that it takes a lot of work. Not just for a while and it's there, constantly you always have to work at it. When either party stops working, the love dies and the relationship ends.