I don't know why that's happening. It's possible you have a defective battery, or maybe even a corrupted iOS version, but I can't say for certain. Having said that, I recommend you make a Genius Bar appointment with the nearest Apple Store and have them diagnose the problem for you.
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.