Definitely not and something like this can happen on every notebook.
On this virtual way it is not easy to say what he problem can be. Suddenly switch offs can be related to high hardware temperature and overheating.
I don’t know how do you use your notebook on battery power supply but I hope you don’t use it on the knees or bed and cooling vents are not blocked somehow.
Place notebook on the desk and check if the same will happen again.
When notebook switches off and you leave it for a while, can you start it normally again?
No response when the power button is pressed, even when using the power mains.
It looks like a serious hardware problem. Usually the notebook would shut down due to high temperature. The notebook supports an overheating protection and if the temperature is too high, the notebook shuts down to prevent the hardware from damage…
Not quite sure if your hardware is affected right now so try this:
Disconnect AC adaptor and remove battery
Wait a some time (view hours 3-4h) then connect both parts again
Then try to power up the unit pressing the power button
If you will not be able to boot up the notebook, you should get in contact with an local service provider.
Did you register the notebook to get 2 year warranty coverage? If you warranty is valid, the notebook should be fixed free of charge.