In sharp contrast with mammals and birds, many cold-blooded vertebrates present homomorphic sex chromosomes. Empirical evidence supports a role for frequent turnovers, which replace nonrecombining sex chromosomes before they have time to decay. Three main mechanisms have been proposed for such turnovers, relying either on neutral processes, sex-ratio selection, or intrinsic benefits of the new sex-determining genes (due, e.g., to linkage with sexually antagonistic mutations). Here, we suggest an additional mechanism, arising from the load of deleterious mutations that accumulate on nonrecombining sex chromosomes. In the absence of dosage compensation, this load should progressively lower survival rate in the heterogametic sex. Turnovers should occur when this cost outweighs the benefits gained from any sexually antagonistic genes carried by the nonrecombining sex chromosome. We use individual-based simulations of a Muller's ratchet process to test this prediction, and investigate how the relevant parameters (effective population size, strength and dominance of deleterious mutations, size of nonrecombining segment, and strength of sexually antagonistic selection) are expected to affect the rate of turnovers.