Im currently using thunderbird for email and it works fine. May I suggest to you to start over again.
1) Make sure in thunder bird that your account are set up by isp standards.
2)Shut off your email program(all of them).
3)Re-instal avast.
4)Run the email wizard, setting it to protect all future accounts and enter in your isp settings.
5)Reboot computer.
6) At this point, I would like you too, if you are using more than 1 email program, to tell one of them to be your default. In my case its thunderbird, it is a much better email client in my belief.
7) Once your email program of choice open up, it will ask you for passwords once again, for each one enter passsword and check remember.
At this point all should be setup. If it is not, I would export your email and your other information to thunderbird, or vica a versa and reinstal the paticular email client that gives you trouble. Again I would use thunderbird for all of this, it just is smotther and oporates much smoother.
Well good luck to you, I hate to see you not use the best av out there for such reasons.
1 last side note, are you using a spam filter for your emails??
Good luck, let us know how it goes