I had a similar problem with the chain dropping and it turned out that the derailleur needed a slight tweak. Shifting etc seemed perfect both up and down, but when rolling backwards or pedalling backwards, it would drop a gear. I think the chain might have been a touch short too with a clutched derailleur. If you have clutched RD, try turning that off and see if the same still happens.
Anyways, I just fiddled with the RD barrel adjustment, and all was good.
HTH
Anyways, I just fiddled with the RD barrel adjustment, and all was good.
HTH