Oh gosh, it's so hard to find a T that's a good fit - but wow. Even once a month seems really really difficult, unless you're very close to finishing up. I hope that they call soon, and make it a priority to get you in.
I'd be really upset about my T canceling on me with short notice, even if it's a good reason. It just is a crappy situation, honestly. It would be easier if she could at least have a plan... like if she'd open up an emergency spot to see you within a couple days.
*hugs* good luck!