Most guys are WAY overbowed with these hard pulling cams we've got today. They start pulling, the arms start shaking from the overload and the arrow vibrates clean off the rest.
There's your 'arrow falling off the rest' problem in a nutshell.
Of course, the guys that use the containment rests like to say they use the rest to keep the arrow from falling off the rest while the bow is on the hanger.