We use a numerical ice-flow model to simulate the response of a 1940s Pine Island Glacier to changes in melting beneath its ice shelf. A decadal period of warm forcing is sufficient to push the glacier into an unstable, irreversible retreat from its long-term position on a subglacial ridge to an upstream ice plain. This retreat can only be stopped when unrealistic cold forcing is applied. These results show that short warm anomalies can lead to quick and substantial increases in ice flux.