In many species, most (or all) offspring are produced by sexual means. However, theory suggests that selection should often favour the evolution of species in which a small fraction of offspring are produced sexually, and the rest are produced asexually. Here, we present the analysis of a model that may help to resolve this paradox. We show that, when heterozygote advantage is in force, members of species in which sex is rare will tend to produce poorly adapted offspring when they mate. This problem should be less severe in species where most offspring are produced by sexual means. As a consequence, once the rate of sexual reproduction becomes sufficiently rare, the benefits of sex may vanish, leading to the evolution of obligate asexuality. Substantial benefits of sexual reproduction may tend to accrue only if a large proportion of offspring are produced sexually. We suggest that similar findings are likely in the case of epistatic interactions between loci.