Maestro, I had a long distance relationship (well, I say long: it was about an hour's drive, but since I didn't drive at the time, it was rarity to see the girl), and to start with she was exactly the same: she was texting me all the time, we'd talk loads, then when we arranged a 'first date', she suddenly started ignoring me, right up until an hour before we were supposed to meet - by which time I had decided not to bother. She made the excuse that she had left her phone at a friends the day before and had only just gone and picked it up.
She said she was sorry, I accepted, and we arranged another date for the following week.
Same thing happened again, with a modified excuse.
By this point I had figured that she was just dead shy - she liked me, but she was terrified about 'dating'.
As I was a complete tool (and I was really into this girl), I kept at it (building comfort etc. by phoning, texting) and eventually we met up quite spontaneously (she seemed to be in a really perky mood one night, we had done loads of flirting over the phone, and I just told her that I was gonna go over to her house that night. And that was that)
However, building comfort to that level did take a few months.

So my advice is that if you are really into this girl, and you feel it's worth the investment, then go for it. But don't chase her - let her figure out when she's ready, and in the meantime, go out and have fun - meet other chicks. Don't get one-itis over her.
You have nothing to lose this way: if she thinks your out having loads of fun, she might get her arse in gear before she misses her chance. On the other hand, if she's not interested, at least you haven't wasted your time chasing her.

Much love,

Craigus