Overheating would be a typical reason for this behavior. What I mean is if the notebook has a higher internal temperature and it will power off immediately to protect the hardware. So it’s normal behavior for overheating.
Overheating can have different reasons. In most cases it’s dust that is blocking the fan. This would mean you have to clean the cooling system of your notebook using compressed air spray to blow out the dust from cooling ventilators.
Usually it should help. If not I would check the display driver. What display driver and operating system you are using?
If you install non Toshiba display driver they can also cause overheating so it’s recommendable using Toshiba’s pretested drivers only.
I agree also but as a slight explanation if the laptop does not have a half desent GFX card then you are using the CPU to do all the work this increases the temp and causes a premature powerdown, clean the cpu cooling fins as sugested and make sure the vents are not blocked failing this turn all the GFX settings down to a minum level so the CPU does not have to work so hard. Typically a 8 - 12 deg increase will cause overheating in most laptops due to game play. you could also look at getting a higher rated laptop with a good embedded GFX card either nvidia or amd with dedicated ram as video ram sharing can also cause prem shut down if you maxed out the frame memory.