Depending on just what you "do" when you "give up" you may end up finally understanding what detaching really means. As I always say, sometimes it takes getting to this point, where there seems to be nothing else to do BUT to detach, or if you'd prefer "give up" before many people get the whole idea of choosing detachment and REALLY doing DB justice.
I am not saying it's the right thing to do but often this state of giving up is what it takes for you to understand just what your options REALLY are.
What I hope you DON'T do is try to force the issue with your W, thinking that your going to give up by way of final ultimatum. If you must walk away, just walk away and try to move on. If you feel you want to issue the ultimatum then I think you are not being honest with yourself that you are "done".