Zimbra 8.0.5
CentOS 6.4

New install as of today. All seemed well at first, then I started experiencing significant queueing problems in the Active Queue, which had me looking at all kinds of possible queueing issues. After a while, my users started complaining about not being able to connect via IMAP, and/or losing their existing IMAP connections. This revealed a whole bunch of messages like this:

2013-10-03 12:02:42,789 WARN [ImapSSLServer-8] [] imap - Dropping connection (max connections exceeded)

in the mailbox.log. So, I increased zimbraImapMaxConnections to 300 (from 200), and things cleared up a bit. A little while later, though, and they started complaining about IMAP again. Again, I saw these messages in the logs. So I bumped zimbraImapMaxConnections up to 500, which again cured the problem for a short while. But, before long, the users were once again complaining. At this point, I've set zimbraImapMaxConnections to 1000, and netstat shows me with 709 IMAP connections (it doesn't look like any one source IP is at fault).

Suggestions, please? Thanks in advance.