Thank you very much, dobsy, for the comments and video.
Is your controller calibrated? Simulated forces can be large enough to "break" the physics engine at which point the plane would not be rendered. Perhaps this explains the plane disappearing. This can happen when controller is not calibrated: arbitrary source values are passed directly to the engine while the engine expects values within the range (-1,1). Please double check that calibration is completed.
Your experience suggest that I should notify user when the physics engine has encountered a problem, if nothing else, to diagnose.
On boundaries, your first run takes the plane quite far from you at a time when, I suspect, you are not applying any inputs suggesting inputs rather than boundaries are doing something funny. Boundaries are actually disabled when entering the game.