Antagonistic coevolution between hosts and parasites is thought to drive a range of biological phenomena including the maintenance of sexual reproduction. Of particular interest are conditions that produce persistent fluctuations in the frequencies of genes governing host-parasite specificity (coevolutionary cycling), as sex may be more beneficial than asexual reproduction in a constantly changing environment. While many studies have shown that coevolutionary cycling can lead to the maintenance of sex, the effects of ecological feedbacks on the persistence of these fluctuations in gene frequencies are not well understood. Here, we use a simple deterministic model that incorporates ecological feedbacks to explore how parasitic reductions in host fecundity affect the maintenance of coevolutionary cycling. We demonstrate that parasitic castration is inherently destabilizing and may be necessary for coevolutionary cycling to persist indefinitely, but also reduces the likelihood that sexually-reproducing individuals will find a fertile partner, which may select against sex. These findings suggest that castrators can play an important role in shaping host evolution and are likely to be good targets for observing fluctuations in gene frequencies that govern specificity in host-parasite interactions.