Here are some tips to help you hang on to your relationship:
1. If she doesn't want to call it a relationship, don't call it a relationship. While that is rather irrational, remember that a rose by any name is just a sweet. By giving her the option of not calling the relationship a relationship, she can maintain a commitment to you without feeling burdened by an official commitment.
2. Don't demand an explanation. You didn't exactly mention this but I would hazard that there are times when she is emotionally distant (quiet, reserved, or half-engaged when you're around) or M.I.A. for hours or even days when you expect to see her or at least communicate with her over the phone or through text. Since she has already told you about her emotional issues, when cases like these pop up, don't attempt to initiate conversation about her strange behavior. She is already aware of her behavior and probably feels bad for neglecting you but she needs that space if she is to be with you. At best, just express how happy you are to see or hear from her. She will appreciate you for your understanding.
3. Even if she never completely resolves her emotional hang-ups, you two can be happy together if you take it one day at a time.
Good luck!