My babies came complete with mites. I am on round 3 now and think I have found a solution. Contrary to what was just posted I understand that they do not breed well in high humidity.
Given that I had read that in various places I took it to be true. So once I made my new babies I started misting them all day long. Never drenched and dries quickly but humidity is obviously high. In fact it is a bit muggy in my room. There were some mites on babies to start with but constant misting has kept them in check now for 4 weeks. This has proven to work much better than neem every 5-7 days. The greatest part is I am using plain cold water.
The side effect is that my babies, which are teenagers now look cartoonishly healthy.
A lot has been said about how to kill mites. The first thing is watch for them. I do not have a problem clipping a fan leaf and disposing of it if I see a sign of mites. This of course guarantees that you killed all of those.
Keep in mind that my girls are in a room with other girls that had a bad dose of mites. After 4 weeks of minimal neem and constant misting, I have had no new infections and seemed to have stopped breeding in its tracks.
I am not that experienced so if someone knows of a drawback to this method please reply.