I don't know of any tools for checking video card memory, and no amount of googling or searching OC-ing or hardware forums has led me to one either. I'm sure that it can go bad, but it's not something that I hear of very often.
What exactly happens when the demo crashes?
Does the computer completely freeze? Does it go to desktop? BSOD? Spontaneously reboot? etc
Are you OC-ing anything? Are you running the demo in DX10 mode? (I don't think the 7900's are DX10 compatible. My EVGA 7600GT KO isn't.)
First I'd run the demo again, and just before you get to the point where it normally crashes, exit to the desktop and check the video card, mobo, and cpu temps. My old shuttle used to artifact and hang and crash like mad when it got a little warm (and it didn't take long with that thing either).
Secondly, it might be worth running Memtest86 and/or 3dMark and/or a Prime95 Torture Test just to see what they dig up. Monitor your temperatures during any of these as well. If you are OC-ing anything, these will let you know if you're being a little over ambitious.
Then, I'd try running another high end game, whatever you've got, and see if you have the same crashing issues on a high detail setting. If all of the above go smoothly then...
Lastly, I'd remind myself that this is a demo so there may still be some hardware compatibility issues to work out before the official release (or afterwards in patches, as is often the case).