That puts a whole different complexion on the entire issue. If you book a date and then book a second one on the same day, at the same time, that's just plain rude. Initially I'd imagined her cancelling due to e.g. illness, or some unexpected work stopping her, or an impromptu family occasion, or a number of unforeseeable circumstances that could well be genuine. If some other friend says to her "hey, want a coffee this evening?" she really should be saying that she can't as she already has something sorted for the evening, rather than cancelling the already-arranged meeting with you.
It suddenly looks a lot worse, anyway, than it did before. I wouldn't necessarily cut off all contact, but I'd certainly be tempted to draw some sort of line about this. It's just rude.