The extent to which parasites are locally adapted to their hosts has important implications for human health and agriculture. A recently developed conceptual framework--the geographic mosaic theory of coevolution--predicts that local maladaptation should be common and largely determined by the interplay between gene flow and spatially variable reciprocal selection. Previous investigation of this theory has predominately focused on genetic systems of infection and resistance characterized by few genes of major effect and particular forms of epistasis. Here we extend existing theory by analyzing mathematical models of host-parasite interactions in which host resistance to parasites is mediated by quantitative traits with an additive polygenic basis. In contrast to previous theoretical studies predicated upon major gene mechanisms, we find that parasite local maladaptation is quite uncommon and restricted to one specific functional form of host resistance. Furthermore, our results show that local maladaptation should be rare or absent in studies that measure local adaptation using reciprocal transplant designs conducted in natural environments. Our results thus narrow the scope over which the predictions of the geographic mosaic theory are likely to hold and provide novel and readily testable predictions about when and where local maladaptation is expected.