Cliv:
I'm assuming you're a man. What others have done is to analyze her, but what about you? What are you getting out of all this? Please know that I'm not accusing you of anything, only to share from my own experience. I ask because I have been in very similar situations before, not so much professionally but socially. You see up until about 4 months or so ago, I would bend over backwards to help out female friends. There were always 1 or 2 "female friends" who got extra attention from me (not sexually, but at the drop of a hat I would be there to help them). After a LONG while, I realized that I often volunteered to help them, even when they didn't ask. Truth be told, these friendships started out platonic enough. But somewhere along the way, I wanted it to be more. I guess I justified it to myself as me wanting to help, but the truth was that I just wanted to start some relationship with them. Thinking back, I was just a jackass for being a doormat and for having other motives. And when all was said and done and it came around for these women to "help" me they were no where to be found. Here's one example, when my car broke down I called and she gave me this "I'm busy" excuse. I should have told her that the next time I can "schedule" an emergency, that I would call her! Needless to say, I won't be calling her anymore, for anything.
I guess I'm wondering what you get out of trying to stay friends with this woman who, your own account, seems to be giving you the brush-off. What ever it is, I hope you find some sense of peace and happiness. Good luck.