It really could be about anything, hardware or software.  Unplug everything unnecessary, even usb things, and just see if it locks up then.  I've had psu's do this, video cards, ram, even usb devices cause weird hardware-ish problems.  Check dmesg and /var/log as well for errors/events, could indicate a flaky device.

Also software - upgrading ram recently, I also updated my system since I had to reboot anyways, and my pc began locking up every 2 days.  I thought the new ram perhaps was bad, but memtest looked ok.  It took some digging, but guess I picked up a bug in using an old intel graphics driver inadvertently, removed that driver, and I've had 70 days of uptime since.

I had to get a bit creative to diag this, including sshing into it from another system when it did lock up.  Turns out it was graphics related, just the display froze, but the system worked otherwise headless.  This led me to investigate graphics as a source of the lockups to fix at a driver level.  If you have another system available, I'd suggest that.

-mb