Climate change has the potential to desynchronize the phenologies of interdependent species, with potentially catastrophic effects on mutualist populations. Phenologies can evolve, but the role of evolution in the response of mutualisms to climate change is poorly understood. We developed a model that explicitly considers both the evolution and the population dynamics of a plant–pollinator mutualism under climate change. How the populations evolve, and thus whether the populations and the mutualism persist, depends not only on the rate of climate change but also on the densities and phenologies of other species in the community. Abundant alternative mutualist partners with broad temporal distributions can make a mutualism more robust to climate change, while abundant alternative partners with narrow temporal distributions can make a mutualism less robust. How community composition and the rate of climate change affect the persistence of mutualisms is mediated by two-species Allee thresholds. Understanding these thresholds will help researchers to identify those mutualisms at highest risk owing to climate change.