Abstract The ice shelves in the Amundsen Sea are being melted rapidly by warm Circumpolar Deep Water (CDW), causing sea‐level rise. Ice‐shelf melt variability is controlled by the speed of a shelf‐break undercurrent which transports CDW onto the continental shelf. We study decadal variability of the undercurrent and ice‐shelf melting using new regional ice‐ocean model perturbation experiments. The perturbation experiments suggest that the undercurrent decadal variability is controlled by variable coastal sea‐ice freshwater fluxes, these driven by winds mechanically opening and closing coastal polynyas. With the perturbation experiments we also quantify a positive feedback mechanism between the undercurrent and ice‐shelf melting which is responsible for 25% $25\%$ of their decadal variability.