You haven't stated which server the problem is with - or whether it's both. You could remove the password from one server and then log in to reset it. Worth a go but not guaranteed to work.

Thunderbird asks for the passwords of the mail accounts each time you log in, even though the checkbox for using the password manager has been set.

First, check if passwords are managed by an external app that is part of some security software. If there are no such apps in use, try this:

Help/Troubleshooting Info, Profile Folder, Open Folder, close TB, rename or delete keys4.db, cert9.db and logins.json, then restart TB, enter the passwords, check the box to store them, and see if they are remembered at next restart.

"Empty versions of those files will be automatically created. Logins.json stores the passwords. The other two are used to store security exceptions. However, they should be considered a set, if you delete one you should delete all three."

http://kb.mozillazine.org/Password_not_remembered_-_Thunderbird