Sex-ratio drive, which results in males siring female-biased progeny, has been reported in several Drosophila species, including D. simulans. It is caused by X-linked drivers that prevent the production of Y-bearing sperm. In natural populations of D. simulans, the drivers are usually cryptic, because their spread has elicited the evolution of drive suppressors. We investigated autosomal suppression in flies from Madagascar, Réunion and Kenya. Autosomal suppressors were found in all three places, indicating that they are a regular component of drive suppression over this geographic area, where strong Y-linked suppressors also occur. These suppressors were suspected of being polymorphic in Madagascar and Réunion and proved to be polymorphic in Kenya. We developed a model simulating the evolution of neutral autosomal suppressors in order to explore the effects of the number of suppressor genes, their relative strength and the co-occurrence of Y-linked suppressors. The most interesting prediction of the model is that when suppression is multigenic, suppressor loci can remain polymorphic despite the absence of balancing selection if an equal sex-ratio is restored in the population before the suppressor alleles become fixed at all loci. The model also emphasises the importance of the sterility of distorters' sons in suppressor dynamics.