This may be a backlight issue. The iPhone 6S does have a well documented history of this problem. When the screen goes black, does the phone appear to be working (receiving calls, text messages, recognized by iTunes)? If so, shine a bright flashlight on the screen to see if you can see a dim image.
That would indicate a backlight issue. It could be screen related or logic board related. Ideally, you would need to test it with a known-good replacement screen to eliminate a variable. Depending on your situation, you could try a screen from a different phone, or have a repair shop try out a new screen. If the screen doesn't fix it, then you will need to have it repaired by a shop that does micro-soldering repairs.