Some of these Pioneer head units "look" for a camera input when they're first turned on. That sets the camera input(s) on or off. If the camera input has been turned on and the deck can't find a camera signal when turned on, it might get confused and shut off. It's a pain, but you can try this:
Connect a camera or cameras to all the video inputs on the Pioneer
Wire the camera or cameras to constant power - not switched power and not reverse/backup light power
Disconnect power to the Pioneer head unit, reconnect power, then reset the head unit
Turn on the head unit and let it go through the initialization process
Go into the head unit's menus and turn on the camera input you want to use - turn off all the other video inputs
Check the owner's manual to see if the Pioneer head unit needs a video signal during startup or if the camera can be wired to reverse gear power (i.e. backup lights)
They make camera power adapters specifically for this scenario that supply a video signal during startup for the head unit. If needed, an adapter like this might make wiring the camera easier. The adapter is usually for OEM radios (such as Toyota) made by Pioneer but they work well for aftermarket Pioneer radios too.