Mass loss from the Amundsen Sea sector of the West Antarctic Ice Sheet has increased in recent decades, suggestive of sustained ocean forcing or an ongoing, possibly unstable, response to a past climate anomaly. Lengthening satellite records appear to be incompatible with either process, however, revealing both periodic hiatuses in acceleration and intermittent episodes of thinning. Here we use ocean temperature, salinity, dissolved-oxygen and current measurements taken from 2000 to 2016 near the Dotson Ice Shelf to determine temporal changes in net basal melting. A decadal cycle dominates the ocean record, with melt changing by a factor of about four between cool and warm extremes via a nonlinear relationship with ocean temperature. A warm phase that peaked around 2009 coincided with ice-shelf thinning and retreat of the grounding line, which re-advanced during a post-2011 cool phase. These observations demonstrate how discontinuous ice retreat is linked with ocean variability, and that the strength and timing of decadal extremes is more influential than changes in the longer-term mean state. The nonlinear response of melting to temperature change heightens the sensitivity of Amundsen Sea ice shelves to such variability, possibly explaining the vulnerability of the ice sheet in that sector, where subsurface ocean temperatures are relatively high.