I've had mine two years with no bungee securing it. Never had a problem. It would take a serious updraft to lift the cover off of the propane. Not really possible, unless you were going over a very high and long bridge with grates. (Bay Bridge over the Chesapeake in MD) Even then I doubt it would move.
On a side note, I recently drove home from a trip on back roads with the pepper shaker sitting on the back bumper. had a good chuckle when my wife showed it to me.
