An asexual lineage that reproduces by automictic thelytokous parthenogenesis has a problem: rapid loss of heterozygosity resulting in effective inbreeding. Thus, the circumstances under which rare asexual lineages thrive provide insights into the trade-offs that shape the evolution of alternative reproductive strategies across taxa. A socially parasitic lineage of the Cape honey bee, Apis mellifera capensis, provides an example of a thelytokous lineage that has endured for over two decades. It has been proposed that cytological adaptations slow the loss of heterozygosity in this lineage. However, we show that heterozygosity at the complementary sex determining (csd) locus is maintained via selection against homozygous diploid males that arise from recombination. Further, because zygosity is correlated across the genome, it appears that selection against diploid males reduces loss of homozygosity at other loci. Selection against homozygotes at csd results in substantial genetic load, so that if a thelytokous lineage is to endure, unusual ecological circumstances must exist in which asexuality permits such a high degree of fecundity that the genetic load can be tolerated. Without these ecological circumstances, sex will triumph over asexuality. In A. m. capensis, these conditions are provided by the parasitic interaction with its conspecific host, Apis mellifera scutellata.