Andrew R Stewart 

Is it possible for you to ride on a quiet street or large empty lot so you can look down at the chain/cassette/rings while starting up (and not hit a car)? Can another ride next to you and watch your drivetrain? What rear cog are you in when the chain drops off the ring? One issue is that thr ring is designed to allow the chain to drop off, that's called shifting when there's a second ring and a der. So the tooth shape doesn't grab the chain as well as a dedicated single ring one would. It's possible that the ring's teeth and chain are so worn that they don't fully mesh and when under power the chain tries to climb up and over the teeth. but this usually doesn't result in a drop. Andy.