Most studies on the biological impact of climate change have focussed on incremental climate warming, rather than extreme events. Yet responses of species’ populations to climatic extremes may be one of the primary drivers of ecological change. We assess the resilience of individual populations in terms of their sensitivity to- and ability to recover from- environmental perturbation. We demonstrate the method using a model species, the ringlet butterfly Aphantopus hyperantus, and analyse the effects of an extreme drought event using data from 79 British sites over 10 yr. We find that populations crashed most severely in drier regions but, additionally, the landscape structure around sites influenced population responses. Larger and more connected patches of woodland habitat reduced population sensitivity to the drought event and also facilitated faster recovery. Having enough, sufficiently connected habitat appears essential for species’ populations to be resilient to the increased climatic variability predicted under future scenarios.