Well, it could be a few things. However I would first look at overheating issues. Try installing monitoring software like "Speedfan" or one of the many others out there and monitor the different temps when the computer turns on, while you are using it, and what it is at when it turns off. You can set most of the programs out there to log the data for you.
If the device is overheating, that will cause it to shut down.