Your relationship is 99% gone.
Make sure that the 1% is a no go, then say goodbye, and if you want to, you can thank her for the good times, before resentment and regret sets in.
It's easy to give advice when you are not in the situation yourself. As point44 says, make sure there is no hope, then say thank you and move on.
But be very careful of that 1%, women can sometimes have emotional swings that men do not(IMHO). It's just barely possible that she may come back and live happily ever after with you. There was one time when my wife wanted to leave me, and I had no idea AT ALL of her intention. After that period, I told her, if she ever felt like leaving me, at least tell me first, so maybe I can do something about it. That was about 7 years ago.
What might make that 1% work is if the main issues she has, are with herself, NOT YOU, sort of like Forest Gump's GF who could not bring herself to stay with Forest Gump because she was messed up from being abused as a child.
But the chances are she just wants out, and there may even be 3rd party, who she may not have slept with, but has her eye on already. I'm sorry, but my understanding of girl's psychology is like that.
I'm not condemning it, it's biological.
If there's no way to salvage it, then let her go and find another girl. She knows you still want her, so telling her by crying, etc is utterly useless.
I'm sorry, but that was horrible advice, IMHO. The only way that advice might be worthwhile is if she is unsure of your love/commitment to her, maybe she wants to legalize the relationship and have children, but you don't/or are unsure, so she's testing you.
It doesn't sound like that, it sounds like she wants out. Leave her, my friend, there is nothing there to stay for.
And if she still wants to talk and so forth, if it is too painful for you, just tell her, it's too painful to talk, sorry, we can't do this anymore. Please find someone else for your emotional backup. And I can't see you either.
The sign that she can still talk, but you cannot with "pain" shows that she is not the one suffering, she's doing what is OK for her(splitting), but it ain't so good for you. Change your heart, there's no place for it with her.
Goodluck on your rebound.