When does my bike chain pop off randomly?

If you brought this bike to me I would first check to see if there were any stiff links. To do this I would put the bike in my work stand, and rotate the crank backwards, looking closely at where the chain runs through the rear derailleur.

I would also ask you about where it comes off the system. Does it pop of the front chainwheel or at the rear wheel. Does it come off on the outside or the inside of the front chainwheel?

The answer to these questions will help to pin-point the cause.

If the chain comes off at the front chain wheel on the inside, then the derailleur "low" limit screw is not in enough. If the chain comes of on the outside, then the "high" limit screw is not in enough.

If while spinning the crank I notice that the chainwheel/chainring is not straight, then THAT could be the cause.

Does the chain come off while pedalling under load? For example when you are standing on the pedals and pushing hard? When cycling up a hill, or when you are changing gears on the front, or on the rear?

Many questions, but all help to troubleshoot the cause.

Also, have you ever crashed the bike, especially on to the right side? This could cause a bent rear derailleur hangar. Which would need to be replaced.

Take a look at ALL of these situations to try to pin-point the cause. If you are troubled, take it to the local bike shop with the best mechanic reputation.