Anthony Calfo suggested halving the anemone, and ensuring it had been kept in excellent conditions for at least six months before propagating. After that, he implied that the recovery time could be as short as a month, but suggested waiting until both halves had mouths that were centered in the anemone again.
The main thing I took from his comments was wait until the anemone is healthy to begin with, and then cut it in half directly across the mouth. Wait until the halves healed appropriately, and then cut again. Once those heal, you now have a healthy group you can begin to frag/propagate on a regular basis if you rotate which ones you cut.
HTH,
Nick