You're not doing anything wrong. THEY ARE. It doesn't matter if it's a tattoo shop. You're a customer, and you deserve good service. As long as you're not walking around being a douche, they should be treating you like a customer.
To me, one strike and you're out--honestly speaking. If they contacted you in advance, apologized, was sincere, contrite, etc...then maybe hey, sure, reschedule. But if they just decided not to show up, or they're pushing you off on someone else, chuck deuces and move on to the next. There are plenty of fish in the sea.
I'd keep researching anyway. Seems as if your hard earned money would be better spent somewhere there are good artists, that show up, show prove, and do their job. That's all.