The maintenance of obligate sex in animals is a long-standing evolutionary paradox. To solve this puzzle, evolutionary models need to explain why obligately sexual populations consistently resist invasion by facultative strategies that combine the benefits of both sexual and asexual reproduction. Sexual antagonism and mate availability are thought to shape the occurrence of reproductive modes in facultative systems. But it is unclear how such factors interact with each other to influence facultative invasions and transitions to obligate asexuality. Using individual-based models, we clarify how sexually antagonistic coevolution and mate availability affect the likelihood that a mutant allele that gives virgin females the ability to reproduce parthenogenetically will invade an obligately sexual population. We show that male coercion cannot stop the allele from spreading because mutants generally benefit by producing at least some offspring asexually prior to encountering males. We find that effects of sexual conflict can lead to positive frequency-dependent dynamics, where the spread of the allele is promoted by effective (no-cost) resistance when males are common, and by mate limitation when sex-ratios are female-biased. However, once the mutant allele fixes, effective coercion prevents the complete loss of sex unless linkage disequilibrium can build up between the allele and alleles for effective resistance. Our findings clarify how limitations of female resistance imposed by the genetic architecture of sexual antagonism can promote the maintenance of sexual reproduction. At the same time, our finding of widespread obligate sex when costs of parthenogenesis are high suggests that developmental constraints could contribute to the rarity of facultative reproductive strategies in nature.