You aren't the only one to be having cookie trouble in IE7. I've spent a lot of time on a related but different cookie issue. Anyway, this is IE7 not Avast. Select "tools", "privacy", and select "advanced". Tick "override automatic cookie handling" and "always allow session cookies". NB this could affect your privacy setting: don't go to any dodgy sites while it's set like this; it's a troubleshoot step. Try it out on this site, and a few others. If it's ok, you can then go back to the privacy settings and configure it for a slick, comfortable blend of privacy and usability.
My problem was to do with a cleanup program. (CCleaner). You aren't using that, are you?