Mavericks mini server won't stay online

My brand new mac mini Mavericks server won't stay online more than about a day or so, and I can't figure out what is happening. I use it for my home network, and our various Macs around the house are registered to the Open Directory server on the Mini for login validation. It also handles TM backups, etc. For the past week or so, the Mini has been mysteriously becoming inaccessible even though it is still powered on. It doesn't happen right away, but usually after it has been powered on for about a day or so. I have the Sleep function set to 'Never,' so I don't think (?) that is the issue. It has a wired Ethernet connection to the network, so not a wifi issue either. It runs without a monitor and keyboard, so I can't easily tell what is causing it to hang up. So far, I have had to resort to holding down the power button to force it off and then restarting, at which point everything works fine again for another day or so until it decides to disappear again. Pretty frustrating. Any ideas on what I might try?

It is possibly panicking, but I don't know for sure since it doesn't have a monitor attached. The last time it happened (yesterday), when I went to reboot it, I noticed the mini was warm to the touch, which I thought was strange, as I don't leave it with apps open or anything. I couldn't imagine what it would have been doing to cause it to get that warm. Anyway, as soon as I rebooted it, once the appeared in the Finder sidebar of one of the other Macs on my network, I did a screen share with the server, and there was a message indicating something to the effect of, "You restarted due to a problem..." (not sure of the exact words), and it asked if I wanted to reopen the windows that were previously open, but I opted not to do that.

I have looked in /Library/Logs/DiagnosticReports, and I don't see anything that appears to be a panic log, but I confess that I don't know exactly what I'm looking for...

Brief update: As predicted, the mini server went unresponsive again after about 28 hours. This time, I left a monitor connected, but I couldn't discern anything obvious that was wrong. However, I did find a panic log. The information in that log was undecipherable to me, but there were a number of entries that seemed like error messages of various sorts.

I decided to bite the bullet and reformat with a fresh install of OSX. That was about 5 1/2 days ago, and so far, everything is running smoothly once again. I wish I knew what happened to cause the problems, but at least everything is normal once again.