Most of the time, my T replies within 1 or 2 work days. Sometimes he doesn't and it's sort of okay when I know that he's busy. But when he doesn't respond all of a sudden after a period of quick replies, it's very triggering for me. I tend to email him again to let him know that I really need a response (and sometimes mention that I feel ignored). Rationally, I know why he doesn't reply and I can understand it, but emotionally it's a whole different ball game.

I can understand why you're frustrated and I'd discuss this with your T on your next appointment. Tell him how it affects you. And ask him to be honest in what he can and can't offer regarding in between sessions.