All users get disconnected multiple times a day

We’re running Openfire 3.6.4 on a CentOS 5.4 box and all our users will randomly get dropped from the server (and reconnect within a few seconds) several times a day. There are several Java IO Exception entries in the log files but nothing that I can make sense of.

What can I check/set to find the cause of, and fix, the disconnects?

xmpp.client.idle is set to -1

Seems to affect all clients (pidgin, adium, digsby, etc)