To survive unpredictable environmental change, many organisms adopt bet-hedging strategies that are initially costly but provide a long-term fitness benefit. The temporal extent of these deferred fitness benefits determines whether bet-hedging organisms can survive long enough to realize them. In this article, we examine a model of microbial bet hedging in which there are two paths to extinction: unpredictable environmental change and demographic stochasticity. In temporally correlated environments, these drivers of extinction select for different switching strategies. Rapid phenotype switching ensures survival in the face of unpredictable environmental change, while slower-switching organisms become extinct. However, when both switching strategies are present in the same population, then demographic stochasticity-enforced by a limited population size-leads to extinction of the faster-switching organism. As a result, we find a novel form of evolutionary suicide whereby selection in a fluctuating environment can favor bet-hedging strategies that ultimately increase the risk of extinction. Population structures with multiple subpopulations and dispersal can reduce the risk of extinction from unpredictable environmental change and shift the balance so as to facilitate the evolution of slower-switching organisms.