We report giant suppression of photobleaching and a prolonged lifespan of single fluorescent molecules via the Purcell effect in plasmonic nanostructures. The plasmonic structures enhance the spontaneous emission of excited fluorescent molecules, reduce the probability of activating photochemical reactions that destroy the molecules, and hence suppress the bleaching. Experimentally, we observe up to a 1000-fold increase in the total number of photons that we can harvest from a single fluorescent molecule before it bleaches. This approach demonstrates the potential of using the Purcell effect to manipulate photochemical reactions at the subwavelength scale.