Sounds like a bad battery to me. My iP 5 has a battery that does sort of that way. Usually when using the camera on cellular. It'll go from 80% to the black screen in a second. But when I plug in, it's back up to around 80%. It seems my camera/FaceTime are the hardest on this old phone's battery.
Sent from my ancient but trustworthy iPhone 5. ☮