With a bit of focused research, I discovered why my machine locked up the second time I ran a GPU program - something that used the 3d graphics. The first time after boot was fine, but if I ran anything graphical after that, it locked up. Turns out that setting the monitor to power off for power savings is what caused it.
Just having the setting enabled caused the video cards themselves to misbehave in SLI mode.
I could either disable SLI or disable the power saving bit. Guess which one I chose? Yup - now when I'm done on the computer, I power the screen off with the power button. And I just played CoH three times in a row without rebooting between games.
How messed up is that? The video cards in SLI would lock the system if power saving was set to turn off the monitor? Weird.