I have the same problem, but it only started a week ago.
POP3 works OK for incoming mail, but not outgoing mail.
IMAP doesn't work at all.
I've tried exporting, deleting and importing the Avast certificate etc.
That didn't work.
Disabling SSL didn't work either.
I've disabled scanning outgoing mail, so I can at least use my POP3 accounts as normal.
The only way that everything works fine is when I disable the Mail shield. But that's inconvenient, to say the least.
Windows 8 Pro 64-bit.
Latest Thunderbird, Avast 8.0.1483.
Latest Comodo firewall.
I've enabled debug logging. If you want the log I can send it to you.