I finally got around to bleaching the microfiber inserts for my pocket diapers. It really seems to have done the trick. No ammonia burn, no noxious smells after just 2 hours of diaper wearing.
I would generally rather use "natural" methods for getting the ammonia stinkies out, but honestly, using a bit of bleach in a 5 gallon bucket was the fastest, easiest, most effective method I've encountered as of yet.
My method was simple: Get a 5 gallon bucket. Add 1/4 cup bleach. Add a bunch of hot water, making sure it's all well mixed. Put in up to 24 "clean" inserts, and let them soak for not more than an hour (really, could probably get away with something pretty brief, like 10 minutes). Run through a wash cycle to get the chlorine out. Done! If you have a top load washer, you could do essentially the same thing in the washer, eliminating the need for a 5 gallon bucket.
How long the benefits will last remain in question, but honestly, I'm going to try not to fret about this and simply do as CottonBabies/BumGenius suggests - once a month or so, wash with a 1/4 cup bleach to keep the stinkies at bay.