After a plesk upgrade without error imap service did not start and found following in maillog:

“IMAP service was down there, it could not start with error

Aug 17 08:00:05 websvr imapd: Invalid -maxperip option.
Aug 17 08:00:05 websvr imapd-ssl: Invalid -maxperip option.”

The reason of the error was that MAXPERIP option was absent in /etc/courier-imap/imapd configuration file. I have added the missed line and restarted service. it  works OK now.