I think it’s not an avast problem, well, in fact, avast cannot handle Hotmail service because it does not work with POP3 and SMTP servers, the way avast scans emails.
By now, can you try using Get Mail 2.3? A desktop application that will allow you to periodically forward on any new mail in your hotmail inbox and optionally bulk mail folder onto another designated account, it works in much the same way as outlook express hotmail access.