Complex sex-determination systems are a priori unstable and require specific selective forces for their maintenance. Analytical derivations have suggested that sex-antagonistic selection may play such a role, but this assumed absence of recombination between the sex-determining and sex-antagonistic genes. Using individual-based simulations, and focusing on the sex chromosome and coloration polymorphisms of platy fishes as a case study, we show that the conditions for polymorphism maintenance induce female-biases in primary sex ratios, so that sex-ratio selection makes the system collapse towards male- or female heterogamety as soon as recombinant genotypes appear. However, a polymorphism can still be maintained under scenarios comprising strong sexual selection against dull males, mild natural selection against bright females, and low recombination rates. Though such conditions are plausibly met in natural populations of fishes harbouring such polymorphisms, quantitative empirical evaluations are required to properly test whether sex-antagonistic selection is a causal agent, or if other selective processes are required (such as local mate competition favouring female biased sex ratios).