Marine ice streams whose beds deepen inland are thought to be inherently unstable. Numerical modelling of the Maguerite Bay ice-stream retreat in West Antarctica since the Last Glacial Maximum suggests that an ice stream can stabilize on an inland-sloping bed owing to increased lateral drag where the ice stream narrows. Marine-based ice streams whose beds deepen inland are thought to be inherently unstable1,2,3. This instability is of particular concern because significant portions of the marine-based West Antarctic and Greenland ice sheets are losing mass and their retreat could contribute significantly to future sea-level rise4,5,6,7. However, the present understanding of ice-stream stability is limited by observational records that are too short to resolve multi-decadal to millennial-scale behaviour or to validate numerical models8. Here we present a dynamic numerical simulation of Antarctic ice-stream retreat since the Last Glacial Maximum (LGM), constrained by geophysical data, whose behaviour is consistent with the geomorphological record. We find that retreat of Marguerite Bay Ice Stream following the LGM was highly nonlinear and was interrupted by stabilizations on a reverse-sloping bed, where theory predicts rapid unstable retreat. We demonstrate that these transient stabilizations were caused by enhanced lateral drag as the ice stream narrowed. We conclude that, as well as bed topography, ice-stream width and long-term retreat history are crucial for understanding decadal- to centennial-scale ice-stream behaviour and marine ice-sheet vulnerability.