OL 7.3 freezing (when idle?)

I'm at a complete loss here, the log files I've looked at don't show anything obviously wrong.

Several of our computers with OL 7.3 randomly freeze up when idle. Typically over night when no one is using them. Sometimes they'll make it to the next morning, sometimes they won't. If we leave a processor intensive process running, it doesn't seem to freeze. We have 4/12 computers experiencing this issue, with no apparent differences between the ones that do and don't. Nothing obvious is showing up in the logs.

Ctrl+Alt+F2 doesn't yield a console (or even a screen wakeup). Alt+SysRq+ (R|E|I|S|U|B) doesn't get any response. System can't be reached by ssh.