Marine-based ice streams whose beds deepen inland are thought to be inherently unstable. This instability is of particular concern because significant portions of the West Antarctic and Greenland ice sheets are marine-based and the resulting mass loss could contribute significantly to future sea-level rise. However, the current understanding of ice-stream stability is limited by observational records that are too short to resolve multi-decadal to millennial-scale behaviour and validate numerical models8. Here we present a dynamic numerical simulation of Antarctic ice-stream retreat since the Last Glacial Maximum that, combined with bathymetric and marine geophysical mapping data, is consistent with the geomorphological record of palaeo-ice-stream retreat. We find that retreat of Marguerite Bay Ice Stream following the Last Glacial Maximum was highly non-linear and was interrupted by stabilisations on a reverse-sloping bed where rapid unstable retreat is expected from theoretical considerations. We demonstrate that these transient stabilisations were caused by enhanced lateral drag as the ice stream narrowed. We conclude that - in addition to bed topography - ice-stream width and long-term retreat history are crucial for understanding decadal- to centennial-scale ice-stream behaviour and ice sheet vulnerability.