Numerical landscape evolution models driven by uniform vertical uplift often develop a static drainage network and a precise balance between uplift and erosion. Small-scale physical models of uplifting drainage basins, however, continually reorganize by ridge migration and do not reach an ideal steady state. Here I show that the presence or absence of persistent drainage migration in a bedrock numerical landform evolution model depends on the flow-routing algorithm used to determine upstream contributing area. The model version that uses steepest-descent routing achieves an ideal steady state, while the model version that uses bifurcation routing results in continually-evolving drainage basins, even under conditions of uniform vertical uplift, bedrock erodibility, precipitation, and landsliding threshold. This result suggests that persistent drainage migration can occur by erosional processes alone. This result has important implications for numerical-modeling methodology, our understanding of the natural variability of landform evolution, and the interpretation of thermochronological data.