If your Xbox controller doesn’t detect any input after X minutes (not sure the exact value), it will go to sleep to save battery. This is the way it’s designed to work and there’s nothing you can do to change that unfortunately. And the behaviour of the Xbox is programmed to pause whatever game you’re running when the controller disconnects. This is what you’re seeing. Even if you’re using another controller like a HOTAS, it will still do this unless there was input on the Xbox controller.
I had this issue as well on PC. I have my Xbox controller attached to my yoke and use it to control cameras and some other functions. After said time elapsed, the controller would go to sleep. Only in my case, it would cause a disconnection event which would cause the sim to freeze for 30-60 seconds and potentially CTD.
The only way around this was to run the Xbox controller with a USB cable to the computer vs going wireless, which prevents it from going to sleep. I suspect that will be the only workaround on Xbox.