Old Mac Pro starts randomly hanging - how do I figure out what's wrong? I have a 2006 era Mac Pro I've been using as a file server.  It's running Lion Server, the latest version, and all software is up to date.  There's very little installed on it beyond the OS.

When I boot it up it runs fine for some random amount of time, then it freezes.  It is headless but I have left screen sharing attached and can confirm that it's not crashing, it just stops responding.

I've got a copy of the system log and there's nothing out of the ordinary in it.  Of course the log is full of errors, as they always are, but nothing is jumping out at me.  The last line before most of the freezes is

Sep 16 19:16:59 mastiff servermgrd[81]: No requests in 300 seconds, shutting down

But from what I can see in Google that's not likely to be causing the problem.

Unfortunately with it being headless I can't watch it boot, so I'm not seeing the boot messages. It's so old I don't have a monitor that will connect to it.

I need suggestions as to how to figure out what's really wrong, so I can determine if it's possible to fix.  Thanks in advance!
Is Lion Server a fresh install, or is it updated from a prior OS? My suspicion is that you're likely suffering from a hardware issue (the only times I've experienced that sort of problem, HW was the culprit), but your first step is to get it running as vanilla as possible and see if you're still having the issue. 

Best bet is borrow a monitor, run diagnostics on the boot drive (make sure the drive isn't dying and the culprit), wipe the drive and install the OS fresh. Confirm you don't have any weird third party hardware connected and see if you're still having the issue. RAM is notoriously finicky, so I'd also look into that (although I admit I've never heard of janky RAM causing this sort of problem) - if the RAM has been upgraded at some point, try just running the original RAM that came with the machine when new. 

If you can eliminate software being an issue, then at that point you'll know a hardware tech (Genius Bar or otherwise) would need to root out the hardware cause.