I am sorry about what you are going through. It is very hard to see a loved one suffering from mental health issues. As it was mentioned before, it does sound like Borderline Personality Disorder.....or possibly both. Either way, it sounds like it would be in your best interest (and in her best interest) if you let things be for now. In other words, go a period of time without contact, because her lack of contact could be a cue that she knows that a relationship is overwhelming for her right now, and she needs time to focus on herself and getting better.

It is so difficult, because I can tell you are obviously very worried about her, and I feel for you. Unfortunately, there is not much you can do right now to help her, because she needs time to figure out how to help herself--which it sounds like she's trying to tell you. If there's any chance for a healthy relationship with her in the future and you give her the time she needs, then she will reach out and respect you for giving her time to take care of her issues. That being said, you need to look out for yourself too. Don't put your life on hold. Work on accepting that a healthy relationship with her is not in the cards at this time and use this time to heal and keep moving forward with your life. It's painful, and I've been in a similar situation with someone I loved (though everyone's situation is different). Take care of yourself. Don't abandon yourself and your own needs.