Weird problem....here's how I would approach things:
1) Hold the card up to the light and try to see if you can see any light showing from under the heatsink. Sometimes, a heatsink can be warped a bit and will not have enough surface area touching the GPU to cool it properly.
2) Pop-off the heatsink and see whether there is any/enough thermal paste or that a thermal pad is in place. If there is a thermal pad, you could take that off and replace it with a bit of Arctic Silver for better heat-transfer.
3) If you can, try replacing your PSU with one that has a bit more wattage. These days, I tend to use 350W and up to allow room for power hungry processors and graphics cards. ( in addition to CDRW's and multiple HD's )
4) If the cpu is overclocked...back the FSB down a bit. Usually, your AGP speed gradually is increased as you raise the FSB. I'm not sure if your motherboard has a fixed rate or a divider to compensate for this...Regardless, raising the AGP speed beyond spec can sometimes cause stability issues.
5) Try raising the AGP voltage to the next highest setting. Perhaps the voltage is fluctuating and dipping below the minimum amount the card can run on.
Give those a shot and let us know how things turn out....Good luck!