http://www.nhm.ku.edu/inverts/ebooks/ch34.html#reproduction
Quote from the link.
"In addition to sexual reproduction, some coelenterates undergo asexual reproduction. Entacmaea quadricolor is one of these. A polyp can divide longitudinally, resulting in two, somewhat smaller individuals, probably within the space of a few days. Each then grows to an appropriate size, divides, and so on. All descendants of the original anemone (the result of sexual reproduction) form a clone, a group of genetically identical individuals. In this species, each polyp is relatively small, but clonemates remain next to one another so their tentacles are confluent, and the associated anemonefish apparently regard them as a single large anemone.
This is so mainly for shallow-water individuals; those in deeper water grow large, and do not divide (see chapter 1). Several other species of actinians also have two different reproductive modes: small animals that clone and large ones that do not. This appears true of Heteractis magnifica, too. In the center of its range (i.e. in eastern Indonesia, on the Great Barrier Reef, in New Guinea), it occurs as single, large individuals. To the east and west (i.e. in western Indonesia and Malaysia, and in Tahiti), several to very many small individuals of identical colouration are typically clustered together, appearing to be a single large (or huge!) anemone. Based on their shared colour and their proximity, we infer that they are clonemates."
A quote from an E-mail I received from Dr. Daphne Fautin.
"And even for the two species of anemonefish host anemones that seem to divide in nature, differences from place to place make me think there may be more than one species of what we think is a single species of each or there may be differences among individuals. Thus, even an anemone that is thought to be able to propagate asexually (*Entacmaea quadricolor*, the bubble-tip, and *Heteractis magnifica*, the "Ritteri" anemone) may die from being cut up."
Just wanted to post something showing that I didn't make the whole idea up.
You may be right. The fact is that we don't know why some of these anemones split and others seem not to. It may be environmental. It may be genetic. There are many possibilities at this point. Who knows?