Androdioecy, where males co-occur with hermaphrodites, is a rare sexual system in plants and animals. It has a scattered phylogenetic distribution, but it is common and has persisted for long periods of evolutionary time in branchiopod crustaceans. An earlier model of the maintenance of males with hermaphrodites in this group, by Otto et al. (1993), considered the importance of male-hermaphrodite encounter rates, sperm limitation, male versus hermaphrodite viability and inbreeding depression suffered by selfed progeny. Here I advance this model in two ways: (1) by exploring the conditions that would allow the invasion of hermaphrodites into a dioecious population and that of females into an androdioecious population; and (2) by incorporating a term that accounts for the potential effects of genetic load linked to a dominant hermaphrodite-determining allele in androdioecious populations. The new model makes plausible sense of observations made in populations of the species Eulimnadia texana, one of a number of related species whose common ancestor evolved hermaphroditism (and androdioecy) from dioecy. In particular, it offers an explanation for the long evolutionary persistence of androdioecy in branchiopods and suggests reasons for why dioecy has not re-evolved in the clade. Finally, it provides a rather unusual illustration of the implications of the degeneration of loci linked to a sex-determining locus.