Today, I fired my .22 AR-build for the first time (it is described in another thread, look for "Bushmaster .22LR upper, RRA NM trigger, and low-mass hammer" as the thread title). I had LOTS of problems: One slam fire (!) upon closing the bolt, a few FTF probably caused by the mag not being exactly in the correct position (the Bushmaster plastic mag seems somewhat out of spec), many failures to fire due to light primer strikes. Most of the time, the rifle was able to eject the spent shell and strip another one and chamber it, but no single time did the bolt carrier successfully cock the hammer. And unfortunately, ARs don't have a cocking handle that doesn't also eject the load (what a pain).
My theory is that the bolt carrier is going too slow, and even though it gets far enough back to operate the extractor correctly, and load the next round correctly, it gets stopped by the hammer, without cocking it.
The thing that's relevant to your question is: I got one doubling. I was testing usually with magazines with 2 rounds in them (for safety reasons, in case the rifle goes full auto on me), and in one case with Winchester Dynapoints (*), both rounds were fired. The cyclic rate seems extremely high, there was no audible gap between the two rounds. My theory is that the second shot was probably a slam fire, or maybe the hammer was pushed far enough back to come flying forward again, but not far enough to latch onto the disconnector or sear. In either case, this could explain the problems you are seeing too: I think the RRA NM fire control system requires the hammer to be pushed back quite far and with considerable power to latch, and with weaker rounds that might not always happen.
The weird thing is that all the other ammo I tried was much more high-powered (Aguila Supermax, CCI Stinger, and CCI Minimag), and I would have expected doubling if any with high-powered ammo. Weird.
Unfortunately, I ran out of time today. My course of action is going to be detail-stripping lower and upper, clearning everything super-carefully again; there seems to be a lot of grit in the moving pieces, and when looking carefully I even found some aluminum filings. Then reassemble and lubricate again. Also, I'm going to try to obtain a weaker hammer spring, or weaken one by bending it. And polish a few moving surfaces with a dremel tool.
(*) Why do I like Win Dynapoints? They are cheap, easily available (Walmart), subsonic = quiet in many rifles, and pretty accurate.
Note: I'm a complete beginner as far as ARs are concerned, so take the above with a large grain of salt.