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Seriously: just stop trying to make one-on-one, time-sensitive plans with Mary. Invite her along for parties, or when you and a few others are going for drinks and will be at the bar for a while. She's clearly fun to be around, just unreliable. And she clearly doesn't need you to be her lap dog. Push her into your periphery and she will almost certainly not even notice--she's got a gaggle of friends, hasn't she?
Don't break a friendship entirely over something as forgivable as flakiness. It's a tolerable, even endearing trait as long as you don't put yourself in situations where you need to rely on the person.