Please upload pictures of your rear wheel area. My chain used to pop off even when tightened, so I had to adjust the chain tensioner to bend the chain just a tiny bit in order to get better grab on sprocket.
roll the bike with drive cover off to see if chain is sticking on drive sprocket (take out plug so you can roll bike) - if that is the problem, you may have to file the teeth of the sprocket so they're a bit more pointy to fit a heavy duty chain
I fixed the problem. I took the chain tensioner off, shortened the chain, and switched the sprocket around so that the lip on it points inward. Now she runs great.