Abstract Recent analyses of climate data indicate that the intensity and frequency of different weather extremes have increased. Such increased environmental variability may lead to increased species extinction rates and hence have important consequences for the long-term persistence of ecological communities. Here we use model communities in order to investigate the relationship between species richness and community persistence in a fluctuating environment. We model two scenarios: (1) correlated species responses to environmental fluctuations and (2) uncorrelated (independent) species responses. We quantify the risk and extent of species extinctions using the so-called community viability analysis. It is shown that species-rich communities are more sensitive to environmental stochasticity than species-poor communities. Specifically, per species risk of extinction is higher in species-rich communities than in species-poor ones. Moreover, for a given species richness, communities with uncorrelated species responses to environmental variation run a considerable higher risk of losing a fixed proportion of species compared with communities with correlated species responses. We discuss the compatibility of these results with the ecological insurance hypothesis.