The two most likely possibilities are overheating and problem with the power supply.
Download HWMonitor and check the temperatures while playing games, you should be worried if the temperatures go over 65 degrees Celsius
For power supply:
You can try testing to see if the power supply is faulty with a multimeter.
If it isn't faulty, it could be not enough power, in which case, you would need to get a better power supply.
I would test overheating first, then faulty power supply. If both of those check out, then I would consider trying new PSUs.