Knowledge of the features that contribute to the persistence of an ecological community is critical in efforts to preserve biodiversity. Food webs, the network of trophic interactions in an ecosystem, provide a representational manner to investigate many such questions about whole ecosystem behavior. Over the past few decades, scientists have begun to develop a clear picture of key components that describe empirical network structure. Nevertheless, the dynamic implications of many these structural features remain to be examined. We investigate the link between food-web structure and dynamics to understand what determines an ecological community's ability to respond to perturbations, such as species extinctions. Whether at the level of individual species or of whole communities, we observe a ubiquitous pattern. The architecture of empirical food webs works to significantly increase their persistence, helping to reconcile the simultaneous complexity and stability of natural communities.