What this error is telling you is that the card has crashed. This is generally a hardware problem. It could be brought on by an excess of heat, a bad overclock, something wrong with the card itself, or something wrong with a part feeding the card (MB or Power). If the card is clean, you are sure nothings else in the system is broken, and the cards are not overclocked then the issue is probably with the cards or the motherboard.
This is a specific error (in a way.. it is also painfully general in that it does not tell you the exact issue) as it points directly to the GPU.
It is very unlikely the problem is with a part of the system unrelated to the GPU (overclock on the memory or cpu for instance). However, SLI or crossfire adds an extra bit of issue to this as cards that work fine alone may have problems together that would trigger TDR.
So my conclusion: this is a Windows problem with drivers and hardware which can only be fixed by replacing the video card with one requiring completely different drivers. Then you can go back to the original drivers and video card without problems (for who knows how long before they become corrupted again).
Something in Windows (Vista & Win 7) is corrupting drivers from both Intel and ATI.