Given the greater chain angles these days it is getting more common to suffer with back pedaling chain drop from the rear's larger cogs to ones smaller. The chain is trying to seek a lesser angle. The simple solution is, of course, don't back pedal
As to the chain coming off when a hard effort is made I would need more data to really figure out the situation. First is where did the chain come off (a simple thing but rather important...) Did the chain drop off all the cogs/rings or just "shift" to another/adjacent sprocket? As mentioned a chain link twist of damage can cause chain drop.
Generally the only time a QR effects this stuff is when it can't maintain the wheel's position in the drop out. This should be simple to check for with a piece of tape indicating where the axle is secured at and thus any shifting from that location. Rear ders also generally don't cause chain drop unless they are twisted, damaged, have very worn pulleys or have really bad SIS adjustment (and also if the cable isn't freely moving along it's path).
More description please. Andy