Webmail probably just quickly opens and closes the connections, so there aren't any connections that are visible for more than a fraction of a second.
On the real issue: I am trying to identify why (just recently) webmail users recently are increasingly facing the error: "ERROR : Connection dropped by imap-server".
The docs I've read on webmail (squirrelmail) affirm your indication that webmail IMAP connections should be closing quickly, so these should not be the cause of the errors.
A few days ago, when I increased the global value of "mail_max_userip_connections", I stopped seeing errors "Maximum number of connections from user+IP exceeded" in dovecot log. However, the above problem continues in webmail.
Don't know if that helps but you could try a local imapproxy like imapproxy from imappproxy.org this should speed up your webmail and reuse connections
Using the command "doveadm who" I see relatively few connections, so I am wondering what may be the cause.
Any ideas will be appreciated!
Thanks, Nick Christian