Just out of curiosity...have you confirmed that the system is shutting down (and not just losing video)?
Sounds like you have additional PCs available. Try enabling sshd on the problem system, and when it "dies", see if you can ssh in from another PC on the network.
I only mention this because I had issues that I misdiagnosed.
On one, the display would flicker and die at random intervals. I thought it was an Xorg/system problem, but I now suspect it is the LCD monitor only, and the system remains running without errors when this occurs. Until I can correct/replace (soemday), that system remains running in a "server" capacity.
On the other (the laptop I'm using), there are definitely Xorg issues (with Intel 945). In this case, a bunch of errors are occuring in the Xorg log, and resetting the display manager doesn't help. However, I am able to ssh into the machine (from another PC beside me), and do a proper reboot. I'll wait for the 2010 ISO (new xorg, kernel, etc) and see if it corrects the problem. Curiously, this only manifests itself while using an external 19" LCD (running undocked, or on the 22" wide LCD at my other office is OK, so far, touch wood).
Maybe this can give you some additional avenues to explore that don't entail much additional cost...