If your tank has only been setup for a month, that's really new yet, and not stable enough for an anemone. While it may appear that you have a stable tank when you test and it constantly shows similar results, the reality is that every tank is very dynamic and will change based on the inhabitants you put in there. With such a new tank, the bacteria which break down ammonia aren't very well established, so swings in water chemistry can happen very easily. At this point, the "health" or water quality of your tank is a knife-edge. Very minor adjustments can send it screaming down one side or another. The longer it has been setup, the more adapted your system is to absorb swings and is more forgiving, and a better environment for delicate animals.