Recombination arrest between X and Y chromosomes, driven by sexually antagonistic genes, is expected to induce their progressive differentiation. However, in contrast to birds and mammals (which display the predicted pattern), most cold-blooded vertebrates have homomorphic sex chromosomes. Two main hypotheses have been proposed to account for this, namely high turnover rates of sex-determining systems and occasional XY recombination. Using individual-based simulations, we formalize the evolution of XY recombination (here mediated by sex reversal; the "fountain-of-youth" model) under the contrasting forces of sexually antagonistic selection and deleterious mutations. The shift between the domains of elimination and accumulation occurs at much lower selection coefficients for the Y than for the X. In the absence of dosage compensation, mildly deleterious mutations accumulating on the Y depress male fitness, thereby providing incentives for XY recombination. Under our settings, this occurs via "demasculinization" of the Y, allowing recombination in XY (sex-reversed) females. As we also show, this generates a conflict with the X, which coevolves to oppose sex reversal. The resulting rare events of XY sex reversal are enough to purge the Y from its load of deleterious mutations. Our results support the "fountain of youth" as a plausible mechanism to account for the maintenance of sex-chromosome homomorphy.