Ross ice streams supply over 90% of the ice volume flowing out of the Ross sector of the West Antarctic ice sheet (WAIS). Stoppage of Ice Stream C (ISC) ca. 150 years ago appears to have pushed this sector of WAIS from negative into positive mass balance <Joughin and Tulaczyk, 2002>. We propose an explanation for the unsteady behavior of ISC using a new numerical ice-stream model, which includes an explicit treatment of a subglacial till layer. When constrained by initial conditions emulating prestoppage geometry, dynamics, and mass balance of ISC, the model yields a rapid (~100 years) stoppage of the main ice-stream trunk. The stoppage is triggered by basal freeze-on, which consolidates and strengthens the subglacial till. Our numerical simulations produce results consistent with a number of existing observations, for example, continuing activity of the two tributaries of ISC. The model always yields rapid stoppage unless we specify ice-stream width that is smaller than its prestoppage values (maximum of ~80 km). We conjecture that if ISC was active for at least a few thousand years before slowdown, its width was significantly smaller than today to sustain the long active phase. Ice-stream width is a key control that helps determine whether ice-stream flow is sustainable over a long term. Our work indicates that the recent stoppage of Ice Stream C could have been part of inherent ice-stream cyclicity, and it leaves open the possibility that other active ice streams may evolve in the future toward rapid shutdowns.