Hi, I'd like to help you with your question.
It sounds like you did all the right things with this girl. You let her know you are there for her and you let her talk to you about her feelings. You've done all you can. The problem here is her. She is not willing to let go and become closer to other people, including you. What you saw with her when you stayed overnight was her willingness to open up and share. But it sounds like most of the time she chooses to be closed off.
From what you said, she may either be depressed or have a personality disorder. Her comment about "being gone soon" says that either she wants your sympathy, or she feels suicidal. If she is looking for sympathy, you may be dealing with someone who has a personality disorder. In that case, she will act out no matter what you do. Personality disorders are often characterized by strong emotions that make it hard to relate to the person in a normal way. They are often hard to treat in therapy as well. Her comment may have been a way to get your attention and have you worry about her.
If your girlfriend is depressed, however, that is something to be concerned about. Letting her parents know you felt she might be suicidal was ok, even if they did not respond (in part, their response tells you why your girlfriend has this problem). Because she will not share with you at this point anymore about her feelings, it will be hard to tell if she truly meant her comment.
All you can do is be there for her. If she does not contact you, let it go. Periodic hello's on Facebook would be ok just to remind her you are there. But if she chooses not to share, there is little you can do to force it. It's hard, I know, to see this kind of trauma going on and feel there is nothing you can do. But people have to want help to accept help. And at this point, it doesn't sound like she is too willing. If you check in once in a while, she may change her mind. And since she already opened up to you, she may be willing to turn to you again in the future. All you can do is wait.
I hope this has helped you,Kate