I understand your frustration about your T not writing back. I've never emailed my T, but I used to call her a lot. Fortunately, she usually called me back within a couple of hours, and often she answered the phone instead so I didn't have to wait at all. But sometimes I had to wait longer, and it was agonizing.

But why should it make you want to quit? Have you ever discussed your T's response time? Maybe your expectations and hers don't match. I'm sure she can give you an idea of how soon she will answer emails.

I'm sorry you're having a hard time.