We investigate whether the recent slow-down of Whillans Ice Stream (WIS), West Antarctica, may lead to its complete stoppage in the near future, using a numerical model. Basal resistance to ice-stream motion is represented by a continuous till layer whose strength changes in response to basal melting and freezing. We implement a basal drainage system, which acts to hinder ice-stream stoppage through supply of extra water to those parts of the bed that are experiencing freezing. The ice module is a standard flowline model with parameterized key out-of-plane effects (Raymond, 1996). The most important result of our modeling effort is that we never obtained a slow-down that would not be followed by a complete stoppage within <100 years. WIS slow-down can be avoided in the model if large basal water-input rates are assumed, to satisfy basal freezing. In comparison, the tested perturbations in WIS width and mass balance had a relatively small effect on the tendency of the simulated ice stream to slow down. These results underscore the need for more quantitative constraints on the efficiency of sub-ice-stream water drainage. We conjecture that the present-day slow-down of WIS will evolve to shut-down in the next few decades, unless an addition of basal water prevents freeze-on-driven bed strengthening.