a. Are you sure it is avast notifying you of a time-out and not your email client?
Note:
I've read about increasing the time-out period but personally I don't think that will help. My problem is with the message prompt -- selecting No should end the connection in my opinion.
b. Do you mean that you haven't tried it, because you don't think it will help?
c. The message prompt is related to the time-out delay.
d. Yes I too would have thought selecting No would break the connection, however there are two elements and I believe the ashMaiSv.exe (Internet Mail provider) will still be trying to complete its scan and hand off to the email client to send it (this I believe will re activate the connection).
Try extending the time delay in your email client as this is most likely to be the first trigger for the prompt.
You might also want to check your Internet Mail settings (reference d. above) to shutdown the connection rather than ask.