Why does my iphone 6 keep cycling on and off?

[iMore Question]

my iphone 6 is cycling on and off,,, about every minute or so it lights up and stays lighted for a few seconds and then shuts down again. It's been doing that for several hours.

 

[Jaguarr40]

Connect to iTunes and restore the phone to factory, reload the current OS and do a back up first please.