Have you tried monitoring the temps on the laptop? You would need to install a monitoring program like "Speedfan" or "HWMonitor" or a few others out there. Then have it log the temps.
What are they reaching just before it shuts down? If it is higher than it should normally be, then that is your problem. Also, if the temps for the CPU, GPU, etc., aren't going up, what about the battery and the charger cord?