I can imagine this would be very upsetting. If it's any help, something vaguely similar happened a few times with my therapist. Then I just realized he is really bad at dealing with emails, and he is much better at keeping track of texts and phone calls. I still use email for some purposes, but if I need a response, I ring or text him. It really helps me to know how to handle this situation, and that I don't have to be stuck helplessly waiting for an answer, which is how I used to feel before figuring it out.

Anyway, not sure if that will help, but just sharing my experience in case it is useful.