Gene drive is a natural process of biased inheritance that, in principle, could be used to control pest and vector populations. As with any form of pest control, attention should be paid to the possibility of resistance evolving. For nuclease-based gene drive aimed at suppressing a population, resistance could arise by changes in the target sequence that maintain function, and various strategies have been proposed to reduce the likelihood that such alleles arise. Even if these strategies are successful, it is almost inevitable that alleles will arise at the target site that are resistant to the drive but do not restore function, and the impact of such sequences on the dynamics of control has been little studied. We use population genetic modelling of a strategy targeting a female fertility gene to demonstrate that such alleles may be expected to accumulate, and thereby reduce the reproductive load on the population, if nuclease expression per se causes substantial heterozygote fitness effects or if parental (especially paternal) deposition of nuclease either reduces offspring fitness or affects the genotype of their germline. All these phenomena have been observed in synthetic drive constructs. It will, therefore, be important to allow for non-functional resistance alleles in predicting the dynamics of constructs in cage populations and the impacts of any field release.