I would expect my T to work an hour late or over the lunch hour or something to fit me in if that happened to me.

That said, I don't think I would quit therapy over it. When I have felt like cancelling all future appointments, I have waited to see if my feelings changed. They usually have; one time I cancelled for the next two weeks; not right after I got mad but still with a couple of days notice. That resulted in T3 calling me to be sure that I was ok. She didn't call right away, it was a week or so into my (unannounced) two week break. I was not in a place where I could talk in much detail or for very long, but I did go back and am glad that I did.