I've backed down and been the bigger person, because I missed their friendship. She chatted to me for 10 minutes on Facebook, then deleted me as a friend and ridiculed my heartfelt apology to all of her other friends on there. The only reason I know this is because we still had mutual friends - who take my side and have decided to freeze her out for being such a cow - so I've given up. It takes two people to be the bigger person, but there's always the need to be the first one to take that step, and I'm happy I found out what she was truly like. I don't want her as a friend if she does something like that!
I'd give her a dose of her medicine, and then after a while has passed offer a truce. If she then rejects you, at least you know where you stand, and you'll be better off without her.
Sometimes though, when someone craps on you over and over again, and you keep saying to yourself, well it's because they're having a hard time because of x, y or z and this goes on for 2 or 3 years and then they do something which is slightly worse than what they've done before - it tips you completely over the edge and you become completely allergic to that person. Anyway, need more details to discuss really.
If she's a grown up, then yes she should be able to discuss issues in your friendship, but it depends what they are, what the background to them is, what implications there are in the rest of her life etc etc etc.
Only you can decide whether her circumstances make whatever it is excusable or allowable. Only you can decide whether it is worth continuing the friendship.