The dropbolt is a good idea. I have seen similar situations where the hole that the bolt goes into isn't sufficiently deep, so it's only extended a quarter inch or so and could easily vibrate loose. If the problem is hole depth, then it should be easy to chisel deeper.

But a bungee does the job for the time being.

Yeah, screws in particle board for a traveling trailer: probably not a good investment, stiff vibrations would pull that apart. You could back the board with real wood and drill into that.