How do I prevent my chain from dropping down while going downhill on bumpy surfaces?
There is no easy and free solution for this, since your bike is not meant to be going downhill.

The best thing you can do is go downhill using the largest front chainring and a pretty large rear cog (but not the largest). This will ensure a pretty good rear derailleur tension which will most probably prevent the chain fall.

If you are willing to spend money on this you could convert to 1x10 or 1x11 (after making sure that the gearing will be good for your rides) and use a narrow wide chainring and a derailleur with a clutch mechanism.