Flowing stream networks extend and retract as their surrounding landscapes wet up and dry out, both seasonally and during rainstorms, with implications for aquatic ecosystems and greenhouse gas exchange. Some networks are much more dynamic than others, however, and the reasons for this difference are unknown. Here we show that the tendency of stream networks to extend and retract can be predicted from down-valley changes in topographic attributes (slope, curvature, and contributing drainage area), without measuring subsurface hydrologic properties. Topography determines where water accumulates within valley networks, and we propose that it also modulates flow partitioning between the surface and subsurface. Measurements from 17 mountain stream networks support this hypothesis, showing that undissected valley heads have greater subsurface transport capacities than sharply incised valleys downstream. In catchments where broad valley heads rapidly transition to sharply incised valleys, subsurface transport capacity decreases abruptly, stabilizing stream length through wet and dry periods.