Email problem: "the recipient was rejected by the server"

I have a website hosted by Inmotion and I frequently use my domain's email.

Several times I have received error messages like these:

"Cannot Send Mail. The server rejected one of the recipient's addresses. The message has been placed in your Outbox."

or:

"Cannot Send Mail. A copy has been placed in you Outbox. The recipient was rejected by the server."

This always happens when I am responding to someone who emailed me. And it almost always happens after the other person and I have already exchange several messages. I simply click "Reply" like before and this happens.

Usually, I can't email the particular address for days, but then I can again. I don't see how the issue could be my settings, considering how inconsistent the problem is.

The problem has always been with ".edu" accounts of major US universities.