If its shutting off at a common length of time from cold, then its probably something to do with IC's overheating or maybe power supply. Maybe try blowing a fan on it while using it and see if it lasts longer. If it does its definitely heat related. In that case it won't be the power supply cable. The problem would be related to items on the motherboard, maybe the capacitors. Its also possible that the heat sink is not attached well enough anymore and it might be a good idea to reseed that. Let me know what happens from there.