1) Check that the chain is the proper (shortest) length
2) Check that the B-tension adjustment on the derailleur is optimal
3) Check that the limit screws for front and rear derailleurs are adjusted properly, in particular the low limit for the front derailleur is as close to the chain as possible with no rub while not affecting shifts (in the small ring/biggest cog combo).
4) Consider installing a chain catcher/keeper.
5) Consider learning to drop off curbs without a significant impact. This is riding style.