Phone shuts down after screen time out

My HTC 816 turns off / shuts down after screen time out. After time out if you let it ideal for 5-7 seconds and then try to wake it up by pressing the power button, you will have to long press the button and the phone will boot.
I also noticed it turns of completely about 80% times and 20% times it restarts.

Other interesting thing i noticed is that if the phone is plugged into a power source it wont turnoff/restart, it will behave as it should.

Also if you are on a call, and the screen times out it wont turnoff / restart.

I guess the problem comes when the phone is left idle.

I have tried factory reset, clearing cache, booting in safe mode, nothing works.

Battery is in very good condition, no fluctuations gives very good backup.