What OS is installed, Win7, 8.1, 10?
Check in Event Viewer to see if there are any critical/error/warning events listed at the time of shutdown that may give a clue as to what is happening.
It may also be a simple heat problem with the hardware.
Check that the laptop's fan vent is clear and unobstructed.
It may be that the fan needs to be cleaned and the CPU may need to have fresh thermal paste applied.
Here's a link to a video that shows how to disassemble your laptop to gain access to the fan so that it can be cleaned.
Here's a link to the ifixit Asus Laptop K43SA A43SA Thermal compound Replacement guide. I realize that it is not your model but it shows how to clean the fan and remove/apply new thermal paste to the CPU which may be of some help, once you have access to your fan and CPU.