In my opinion, it is impossible to eliminate Aiptasia completely. Only boiling the live rock would help.
Aiptasia live inside the crevices of the rock when very small.
There, only the Berghia nudibranchs can reach them. Those nudibranchs eat with preference the small and hidden Aiptasia because Berghia nudibranchs stay hidden, too, most of the time as they want to avoid predators.
Peppermint shrimp and copperbands eat the bigger ones but as people report it often takes some time and can be somewhat unpredictible as both eat other things, too, while Berghias live only from Aiptasia (and near relatives).
Apart from the usual sexual and asexual reproduction it is said that a new Aiptasia emerges from the pedal base that a moving Aiptasia leaves behind. So, this would mean even the smallest Aiptasia would reproduce asexually.
I saw that the Berghia nudibranchs in the crevices of the rock do their work but it's never enough to eliminate all of them. Also, they clean up mostly the shaded parts of the rock only. But that's quite helpful as in those parts live tubeworms, sponges, and ball anemones, and they protect those animals with their work while I can concentrate on eliminating the more exposed Aiptasia that are easier to reach for me.
It also doesn't make sense to combine Berghias with peppermint shrimps as those shrimps are predators of Berghias. The only defense mechanism of Berghias is to store stinging cells (nematocysts) of the consumed Aiptasia in their cerata (the typical outgrowths on the body of nudibranchs) and throw off their cerata when threatened.
But as peppermint shrimp eat Aiptasia, too, this defense doesn't work with peppermint shrimps.
I only noticed that I got Aiptasia infested live rock from one particular LFS (in Leeds) while the other (Fish People in Keighley) sold me on four occasions Aiptasia-free live rock. I don't know how they manage it but they have a large display tank with no Aiptasia and no Aiptasia eating critters in it. They sell often live rock directly from that populated tank (fish and simple leathers) and add new live rock to that tank but never have got any Aiptasia, so far.
