My initial thought, reading your question, was to stick with this T but keep actively searching for another (better) one. As in, better to have someone than no one at all.

Reading on: it seems she is not hearing you and her approach doesn’t seem to be what you are looking for. Thus, if you are profoundly unhappy or dissatisfied, it might be best to take a break from therapy.

That being said, I don’t see that she did anything wrong re the flaky issue. What else can anyone do if others are flaky.. Flakiness is not something we can predict nor control. There is not much choice when in a relationship with such people: either we accept their flakiness and adapt expectations etc. accordingly, try and talk to them (but they might not want to change) or reduce/cut contact. What else is there to do...?