SRAM Eagle issue..

Check how bent the chain is in your largest gear - that is a very common issue with 12-spd systems. It isn't running straight so will be likely to 'drop' as it tries to straighten and then can run off the cassette teeth.

It tends to be less of an issue with brand new drivetrain bits and a Shimano or SRAM chain tends to be less problematic.

Aware that isn't going to be helpful, but I don't know how to fix it, just reduce it.

Have a check of your mech dropout alignment. I had this problem with my SRAM eagle 12 speed on a new bike and after a year of the chain dropping down off the largest sprocket I finally checked the dropout and it was out. Not a massive amount, but with 12 speed it needs to be spot on. Not had a problem since.

First check would be the mech hanger as above, then how worn/wobbly are the jockey wheels?

1. Check hanger alignment with a proper tool like a Park Tool DAG (or get your LBS to do it). 9 times out of 10 this is the issue with 12 speed, as someone said above. Needs to be absolutely spot on.
2. Check and set correct B tension (under sag) using the SRAM Eagle B tension guage.
3. Confirm chain length is correct using SRAM method (even one link more or less can throw things off on some frames).
4. If still issues then replace inner and outer gear cable and check routing is all ok.
Even then, the back pedal issue can happen on some frames but the fact that all has been ok for you previously points to one or more of the above.

I had same a while back, mech hanger and bottom cage straightening sorted. But a number of useful checks above to run through. 

If it's a back pedalling issue that wasn't there previously, I'd look at your freehub. If that's getting sticky, then it might be the cause. A clean and reliable of your pawls might help and never hurts anyway.

Forgot to mention that if all of the above advice fails to return you to shifting bliss then check out https://madronecycles.com/products/super-shims

In my experience it isn't an issue with X01 / XX1 rear mechs but if you have a GX derailleur and it's a few years old then they can develop some play. Easy fix, as above. 

I've got a curious issue with a hybrid GX cassette/chain + SLX shifter and mech system, which worked perfectly until recently. Now I notice that occasionally if I shift a couple of gears down the cassette but don't immediately pedal to lock in the new gear, it feels like it jams up and chatters in every gear, and sorting it involves a couple of backpedals which pull the mech forward and eventually the chain 'releases' and resumes normal service.

Worn jockey wheels, maybe? They look fine and there's no extra play in them. It did it with an older chain, and with the new one that replaced it.

I had weirdness going on at the back end too. The freehub was a bit sluggish when freewheeling and causing a bit of sagging in the chain. All the usual checks as above were fine. At the end of the ride it was obvious that allt least one drive side bearing was booked. I removed the cassette to find that the freehub bearings were great but the drive side wheel bearing was trashed. I replaced them all seeing as the hub was in bits and life is now sweet again. All in all it took me about an hour. The worst bit was getting the bearing caps off.