Many people are very selfish and appreciate people when they do things for them, such as lending an ear, but have no interest in them otherwise. People like to talk about what upsets them in the way you describe. It seems to be particularly common in females, as others pointed out.
You must examine yourself to see if you are making it too easy for her to do this. You are probably a good listener who does not demand much of her. Perhaps if you explained that you do not appreciate the way she treats you, create some boundaries, or express problems of your own, you will grow a better friendship. However, you may very well lose her completely. I am not sure how much of a loss that would really be though.
This often happens to me, and it is my own fault. Human beings are my main special interest, and it is hard for me to pass up a new subject. I encourage people to talk to me about all of their problems, even without realizing it at times because I want to study. I like helping them sort through their problems, but of course, once they are sorted, they have no need for me. I had not even tried to associate with people in a way other than for studying them until a few years ago, so I really do not know how to. Because I use my old "research" methods to start relationships, mine are usually not very good. Most of my social relationships are very therapist/client or scientist/study subject in nature.
I would imagine many people on the spectrum would either try too hard to please other people because they want to make friends badly, resulting in them acquiring selfish friends who take much and give little, or that some people on the spectrum would be the listeners because they are too cautious about annoying people with obsessive topics and do not know how to respond in a "normal" way.
Oh, advice... If you are not happy with the friendship, there is no reason to keep it. If she is using you when she wants you, and ignoring you at all other times, it is not a healthy relationships. Unless you can explain to her how you feel and she changes, you should not let yourself be in such an unfair situation.
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While Mr. Kim... has fallen prey to the inexplicable need for human contact, let me step in and assure you that my research will go on uninterrupted, and that social relationships will continue to baffle and repulse me.
- Dr. Sheldon Cooper (TBBT)