Because of the twofold cost of sex, genes conferring asexual reproduction are expected to spread rapidly in sexual populations. However, in reality this simple prediction is often confounded by several complications observed in natural systems. Motivated by recent findings in the Cape honey bee and in the parasitoid wasp Lysiphlebus fabarum, we explore through mathematical models the spread of a recessive, parthenogenesis inducing allele in a haplodiploid population. The focus of these models is on the intricate interactions between the mode of parthenogenesis induction through automixis and complementary sex determination (CSD) systems. These interactions may result in asexual production of diploid male offspring and the spread of the parthenogenesis-inducing allele through these males. We demonstrate that if parthenogenetic females produce a substantial proportion of male offspring, this may prevent the parthenogenesis-inducing allele from spreading. However, this effect is weakened if these diploid males are at least partially fertile. We also predict a degradation of multilocus CSD systems during the spread of parthenogenesis, following which only a single polymorphic CSD locus is maintained. Finally, based on empirical parameter estimates from L. fabarum we predict that male production in parthenogens is unlikely to prevent the eventual loss of sexual reproduction in this system.