West Antarctic Ice Sheet loss is a significant contributor to sea level rise. While the ice loss is thought to be triggered by fluctuations in oceanic heat at the ice shelf bases, ice sheet response to ocean variability remains poorly understood. Using a synchronously coupled ice-ocean model permitting grounding line migration, this study evaluates the response of an ice sheet to periodic variations in ocean forcing. Resulting oscillations in grounded ice volume amplitude is shown to grow as a nonlinear function of ocean forcing period. This implies that slower oscillations in climatic forcing are disproportionately important to ice sheets. The ice shelf residence time offers a critical time scale, above which the ice response amplitude is a linear function of ocean forcing period and below which it is quadratic. These results highlight the sensitivity of West Antarctic ice streams to perturbations in heat fluxes occurring at decadal time scales.