Thunderbird exceeding the maximum number of IMAP connections
As with all precision engineering, a large sledge hammer is sometimes required for delicate adjustments.
Changing the IMAP password used by Thunderbird is a case in point.
A typo when entering the new password into Thunderbird resulted in the email server suspending the account... ho hum.
Should be simple enough to resolve... close Thunderbird, re-enable the account on the email server, restart Thunderbird, attempt to connect again (this time with the correct password) and..
Unable to connect to your IMAP server. You may have exceeded the maximum number of connections to this server. If so, use the Advanced IMAP Server Settings dialog to reduce the number of cached connections.
After changing the "Maximum number of server connections to cache" on the advanced tab of the server settings dialogue, clearing out the save passwords in the Options tab, restarting Thunderbird multiple times the error message was still being displayed.
In desperation the computer on which this copy of Thunderbird was executed was restarted... and the problem was solved!