Yes, in my younger years, a therapist I saw for a short time fell asleep in our session. He was teaching me progressive relaxation and I wasn't really struggling with it. My entire body was in a knot of tight muscles (totally contrary to what the tape was instructing). My therapist didn't say anything so I opened one eye to peek at him and there he was in all his glory, snoozing away. I didn't wake him up, he finally lifted his head. I never mentioned it but I didn't go back. I wasn't making much money back then and it infuriated me that I was paying someone to sleep. It sounds as though you have a good relationship with your therapist so leaving might not what you want to do. If he doesn't keep doing it and he certainly feels bad that it happened, you might want to chalk it up to a one time thing.

Sure hope you're feeling better. I have sudden bouts of tachycardia too--not really related to anxiety though. I'm lucky though I don't really feel them. Hope your doc is able to help!