So, is the chain coming off the crank, I gather? Which way? If you're loosing it off the big ring, then first thing is to check the limit screws for the DR. If the little ring, likewise, except that you can also get good old mountain-biker's "chain suck" from any number of things, from insufficient tension on the chain (from the rear DR springs) to having the chain be a bit too long to just being all crudded up and and adhering to the chainring.
Sounds like your shifting practices might be a bit suspect... On my old police patrol bike (a Trek MTB) I got chain -suck rather often till I started shifting onto the little ring only slowly and deliberately.