There could be many reasons for why your girlfriend deletes her messages! I don't think you should jump to conclusions right away... Instead, here's some advice that should help you decide what to do next:
1. The first thing I'd say is that if you know that she is deleting her messages, I'm guessing you have access to her Facebook account, and that she knows that you do? She may be deleting her messages because she doesn't want you to see them, not because she has anything hide, but just because she values her privacy.
2. I really don't like the idea of someone reading my texts, emails or Facebook messages. It doesn't mean I'm saying bad things about anyone, or that I'm doing things I don't want people to know about, it's just a peace of mind thing. What I say to someone I like to keep within a conversation so it can't be taken out of context. Could this be the case with your girlfriend?
3. If you are reading her messages and she is deleting them it sounds as though maybe you guys have a few trust issues? You should try and talk to her about this. Who knows- maybe she's deleting her messages because they're all about how much she likes you and she's embarrassed about it! There's just no way of knowing unless you discuss how you're feeling.