I had this exact problem which started a couple of weeks ago but is now solved - the problem was one of overheating. I managed to resolve the problem using two free software utilities.
I'd be working away and (around mid-afternoon usually) my Mac Pro would unexpectedly shut down. Actually, not shut down - just turn itself off as if there was a power-cut. Then it would restart itself and be OK for a while.
My first thought was that it might be related to the graphics card; it has eaten one before and the problem seemed to be worse when more than one monitor was attached. I called a local computer guy who has helped me with the Mac Pro before - and he suggested that it might be the power supply at fault. The problem here is that you could start throwing money at replacing parts, whilst not really knowing whether or not it's going to fix the issue.
The other thing he suggested that might be the problem is that it was overheating. This seemed to be a reasonable guess, as the studio is pretty warm and the power-downs seemed to occur later in the day, when the machine had been running for a while. I asked him to order a new graphics card anyway, but investigated the overheating issue while I was waiting for it to arrive.
The first thing I did was a search on Google for Mac Pro temperatures. The first utility I found was Hardware Monitor (shareware) - http://www.bresink.com/osx/HardwareMonitor.html
This shows the current temperature of every component that has a sensor in the computer. The hottest thing in my list was the Northbridge Heat Sink which was getting up to 88°C (190°F). A small amount of research made it clear that this was a bad thing... if the heat sink was this hot, how hot must the chip have been? The Northbridge Chip ships with a thermal paste applied. Over time, this can literally 'bake' off, resulting in hotter operating temperatures. If it gets too hot, the computer powers off.
This also explains why the internal fans weren't kicking in sooner - they're set at a default idling RPM which eventually just isn't enough to prevent the overheating.
Enter utilty 2 - Fan Control (freeware) - http://www.lobotomo.com/products/FanControl/
Once installed, this utility is accessed via the System Preference pane.
I downloaded and installed this (while the Northbridge Heat Sink temperature was topping 88°C again) and the fans instantly kicked in - in a big way. They brought the sink temperature down to about 45 / 50°C. I set the minimum fan RPM to 1000 and the upper and lower thresholds to between 40°C and 70°C.
By this time I was down to one small monitor, and after a couple of days of no problems, I put my 30" cinema display and additional 19" monitor back on - and waited. That was 10 days ago and the problem has vanished - and as far as I'm concerned, solved. I hope this works for you.
