I agree that it is normal, even reasonable, to feel rejected when someone doesn't respond to communication. I don't necessarily agree that it is the same as being "ignored," especially when we are talking about email and particularly when someone has actually said they will not reply. Feeling ignored and being ignored are two different things.

I also think it can be helpful to develop a sense that the way others respond to us will not necessarily just be about us, and our worthiness, but about the person who may not have time or inclination to respond. I think good therapy challenges one's assumptions about meaning in the world. People can like and love you deeply but still not want to reply to your emails. Perhaps it is better to develop a robust sense of what it means to be ignored or not ignored, and to develop better coping when people don't respond as you would like them to. I don't believe that healthy communication requires anyone to reply to an email, or anything else. In the past several weeks I've discovered the freedom of blocking three people from my cell phone. All three of them wanted me to do different things for them that I didn't want to do, and I didn't want to have to get into a discussion about what I wasn't willing to do and why. In or out of therapy, nobody owes anyone a response to any kind of communication. In therapy, you are not entitled to it just because you pay for time in a session. The sort of entitlement that therapy clients have should be examined in session.

So I think not receiving an email reply is a problem for the client to deal with, and not an argument that a T should reply to emails, especially when the client has not raised any discussion about whether email correspondence would be permissible (and because T's charge by the hour, whether it should be paid for). I think if a client desires email communication, s/he should ask about the parameters of that communication, not just assume and expect things without checking them out with the other person.