Now, I'm also not informed when it comes to asexuality but I do know that talking can be very difficult, no matter what gender/sexuality. I can relate to your partner on this aspect, as I also have this issue when being in a relationship. I tend to keep feelings and problems to myself and just don't like opening up on them. Even though communication is key, like NatJones and Arkhi have already mentioned, I think you should go slow on engaging conversations about problems she has. It could feel to her like you're pushing too much very quickly, even though you think you aren't. Maybe you could try to just take it easy with each other for a while, so you can both focus on yourselves. This could free your minds. Then have a chat with her in a coffee house or another neutral place and start from the beginning.
If she is struggling with her sexuality, I think you should let her discover herself (and so should you for yourself). One of the reasons for her behaviour could be that she's suffering from an internal conflict. If that's the case (and I don't mean to scare you here), she will probably eventually open up to you if she really loves you.