I haven't had a chance to track this down yet but thought I should ask if anyone else is seeing something similiarly.
It seems like RoundCube is leaving IMAP connections hanging. I haven't had a problem with SquirrelMail, but using RoundCube appears to eat up the connection pool preventing further connections until restart/timeout.
When I can find the time I plan on going over the logs.
I'm using Courier-Imap.
~Rob