Spatial rarity is often used to predict extinction risk, but rarity can also occur temporally. Perhaps more relevant in the context of global change is whether a species is core to a community (persistent) or transient (intermittently present), with transient species often susceptible to human activities that reduce niche space. Using 5–12 yr of data on 1,447 plant species from 49 grasslands on five continents, we show that local abundance and species persistence under ambient conditions are both effective predictors of local extinction risk following experimental exclusion of grazers or addition of nutrients; persistence was a more powerful predictor than local abundance. While perturbations increased the risk of exclusion for low persistence and abundance species, transient but abundant species were also highly likely to be excluded from a perturbed plot relative to ambient conditions. Moreover, low persistence and low abundance species that were not excluded from perturbed plots tended to have a modest increase in abundance following perturbance. Last, even core species with high abundances had large decreases in persistence and increased losses in perturbed plots, threatening the long-term stability of these grasslands. Our results demonstrate that expanding the concept of rarity to include temporal dynamics, in addition to local abundance, more effectively predicts extinction risk in response to environmental change than either rarity axis predicts alone.