Right stick shuts off controller

that would likely indicate a short inside of the controller and you'll need to replace it

If the controller is not receiving any input it will time out and shut off. Every now and then you need to move a stick or do something with the controller to prevent it from timing out and shutting down.

Yeah, it does suck. I feel your pain. I can't tell you how many times it's cut off during a match when running the second controller on wifi. I'm pretty sure if you plug the controller in though it won't shut off. That or you have to remember to move the
analog stick on the controller. I try to bump an analog stick after every match to make sure it doesn't turn off.

Not to my knowledge. After having to change the batteries on my last controller it started with the right stick issue so i started checking into it. After a few hours of that i shut it down.

Coop mission/ switch your heli controls to legacy(I think, I can't remember off the top of my head). It makes the roll on the left stick and the up/down, left right on the right stick. Easier to manage.