Bugzilla

I agree that it doesn't seem to be a tls problem when you see the same error with pure tls on port 993 too.

Looking at your original attached log and the pasted log in comment 0, it appears that something is happening to the 2nd dovecot connection before the login is attempted. It is wanting to do a folderstatus on your Entw%26APw-rfe folder (Drafts in mutf7 encoding). Not sure why a "folderstatus" URL is happening first but the log was recorded with tb 45 so maybe that was typical then. Maybe an updated log would help using your current version of tb.

A possible way to determine what is going on would be for you to provide me with a temporary test account on the same server. If that's possible you can send the credential via my bugzilla profile email address.

If that's not possible, could you record a new IMAP:5 log with accounts on non-problem servers disabled by un-setting "check for new mail on startup", "check for new mail every x minutes" and "immediate notification". Select Inbox on the problem dovecot account and shutdown tb and then restart tb with the env. vars set to record the log file as described here: https://wiki.mozilla.org/MailNews:Logging. Don't select any folders in the non-problem accounts while recording the log. Let tb come up selected on Inbox of the problem dovecot account. Then move to another folder (maybe Entw%26APw-rfe or whatever) until you see the error. If no errors seen, shutdown tb and try again until you record a log with the error. 
If and when you attach the log, please described what you were doing while recording it.

It looks to me like either the server or tb is dropping the connection before the authentication even occurs. But it's not clear to me if you are seeing a prompt to enter the password or what the user-level indication of the problem is.

I agree that it doesn't seem to be a tls problem when you see the same error with pure tls on port 993 too.

Looking at your original attached log and the pasted log in comment 0, it appears that something is happening to the 2nd dovecot connection before the login is attempted. It is wanting to do a folderstatus on your Entw%26APw-rfe folder (Drafts in mutf7 encoding). Not sure why a "folderstatus" URL is happening first but the log was recorded with tb 45 so maybe that was typical then. Maybe an updated log would help using your current version of tb.

~~A possible~~ The best way to determine what is going on would be for you to provide me with a temporary test account on the same server. If that's possible you can send the credential via my bugzilla profile email address.

If that's not possible, could you record a new IMAP:5 log with accounts on non-problem servers disabled by un-setting "check for new mail on startup", "check for new mail every x minutes" and "immediate notification". Select Inbox on the problem dovecot account and shutdown tb and then restart tb with the env. vars set to record the log file as described here: https://wiki.mozilla.org/MailNews:Logging. Don't select any folders in the non-problem accounts while recording the log. Let tb come up selected on Inbox of the problem dovecot account. Then move to another folder (maybe Entw%26APw-rfe or whatever) until you see the error. If no errors seen, shutdown tb and try again until you record a log with the error. 
If and when you attach the log, please described what you were doing while recording it.

It looks to me like either the server or tb is dropping the connection before the authentication even occurs. But it's not clear to me if you are seeing a prompt to enter the password or what the user-level indication of the problem is.