I'm lucky to have a T who gets back to me ASAP with emails. However, there are days she doesn't get to them until right before leaving. If I need her to get back to me ASAP it is best to call and leave a message indicating so. I have an understanding that she can ONLY reply if her schedule allows. There are times she reads through the emails, but then a client shows up, and she forgets to respond to those she's read. She is only human. To be able to use this communication with her, I had to agree that I understand that if she does not respond I do not take it as ignoring or abandoning.
I think the best thing to do is discuss email with her. She may not know you want a response every single time. She may read it and take it as an FYI - something to know inbetween sessions. You have to be very clear with your needs, and request she be very clear with what your expectations should be.