I had the same problem and ended up calling support.
In my case, only outgoing was affected. For Thunderbird, the fix is to open the main screen, click on the security tab, then click on the mail shield tab, then click on settings and uncheck scan outgoing mail.
Avast8 can now handle the SSL emails without having to modify your email settings in your email program.
If you previously had avast 7 you will have needed to change your email program, account settings to allow avast to scan SSL email, these changes need to be reversed, e.g set back to the SSL ports and Authentication.
Delete the entries for your email accounts in the avast Mail Shield > Settings > SSL Scanning.
Configuring Thunderbird and avast! Mail Shield.
Check out the above I don’t know how they would relate to your “self hosted cpanel” use of thunderbird.