Avast scans your emails being sent or received, during that period, there is no activity between the computer and the email server/internet, so there is a timeout warning, that's it.
What would be more helpful would be the exact timeout message or a screenshot of it so we can identify if the timeout is legitimate?
What is your email program?
What were you doing when you received the error, senting/receiving email, just browsing, etc?
Do you use Azeurus or any other P2P program, if so what one?