I don't email my T but this would drive me crazy too.

If you need a way to communicate with her when you really really need her, then you need to establish that means with her. For example, can you leave a phone message occasionally for her to call you back? Or will you be tempted to leave them all the time? Can you let her know in an email if this is one time that you really need to hear back from her?

(((((Moonkin)))))