A girl I like always randomly leaves the facebook chat without saying a word !!!?

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I've met this girl about 2 months ago in trip with one of university's clubs. Before meeting her, I was always catching her staring at me and she would look away as soon as I catch her.

I tried to talk to her over facebook for three times, after some 4 to 6 messages she would randomly drop the conversation without saying something and it drives me crazy !! She seems excited when answering me but ...
She would check the message the day after and not word given.
When I meet her in the hallways of the university, she would always smile and say a cute hi to me.
I'm a kind of shy guy who wants to do things slowly, I mean get to know her a little bit before asking her out but she doesn't give the chance to know her.
During the three conversation I was the one starting the conversation just talking about random stuff, trying to engage a conversation to get to know her.
I complimented her for about three times in real life and she took them with a large smile saying thank you ( even on facebook)
Don't know what to do with this girl ?? It has been two since I've talked to her on facebook, convincing myself that she would put the effort to talk to me first for a while.