Beleive it or not, I have the same problem at work. I havent figured out what it is yet (though I beleive its something with Red Hat and its software - bet that it would not happen with Slack ) (I dont have how to prove that though =/ ). The server silently stops responding, no panic, no nothing.
The next thing I will do is diabling APM (Advanced Power Management) support: apmd is the deamon and there is also a kernel module. I have seen lots of PCs panic'ing and freezing because of APM. Check that in your server (you dont need your server going to sleep also).
Hope it helps (and hope we both get our problems resolved with that =) )