Actually shutting down after 20 minutes of play sounds more like either the video card or CPU overheating and shutting itself down to protect from damage or an underpowered PowerSupply reaching a higher temp and losing a bit of its output shutting the system down due to a lack of clean power to supply the needs of the system.
How long has it been since you cleaned the inside of the system (dust buildup causes heat build up) -- Is the PSU the original to the system and you've upgraded the Video card to a more power hungry card ?