If the supply does have a problem or some hardware is heating up other then the cpu it could be pulling power to ground after a period of time goes by. You may not spot a high temp for it in the hardware monitor on the board as well as using something like SpeedFan to look over cpu, board, and drive temps. Besides hardware incompatibility being possible drivers are another to look at.
A 4x card however should be a 4x/2x card backward compatible if the card itself is not seeing a problem. An 8x card is generally an 8x/4x card for use on older AGP boards. A look at the overheat protection options seen in the bios will show if the shutdown or restart temps are set too low? That would usually see or sound an alarm with a beep code.
A defective or weak battery will also see problems with sudden restarts. If you have been running the case for over a year's time the Lithium battery found on the board itself may be starting to go on you being too weak. One day it may simply not start up due to that. A $2 watch battery can trip you up as well as some other failure.