Does it happen even while it's plugged into its AC adapter? Please do try these troubleshooting steps that may help.
- Do a hard reboot first, remove the battery and unplug the AC adapter then press and hold the power button for 20 seconds then try observing it again.
- If it will still shutdown automatically, remove the built in battery and connect it directly to its AC adapter and observe if it will still shutdown by itself.
- Next to try if it will still shutdown is to try a different AC adapter that has the same voltage.
- If it will still not work, I would suggest opening the laptop again and remove off the dust off the fans and apply new thermal paste onto the CPU.
- If all these will not work I would suggest contacting ASUS for a repair specially if it's still under the factory warranty.