That is up to you.

If you don't try, it'll be easier to heal faster and get over it and on with your life.

If you do try, you might win her back, but if she continues to be like this, it might just prolong the current situation, which is obviously not what you want.

My advice:
tell her to choose. Either she chooses to try it with you, or she chooses not to. Neither of those choices are definitive and binding, it's just a relationship. But she most choose now.