Cortical populations often exhibit changes in activity even when behavior is stable. How behavioral stability is maintained in the face of such "representational drift" remains unclear. One possibility is that some neurons are stable despite broader instability. We examine whisker touch responses in superficial layers of primary vibrissal somatosensory cortex (vS1) over several weeks in mice stably performing an object detection task with two whiskers. While the number of touch neurons remained constant, individual neurons changed with time. Touch-responsive neurons with broad receptive fields were more stable than narrowly tuned neurons. Transitions between functional types were non-random: before becoming broadly tuned neurons, unresponsive neurons first pass through a period of narrower tuning. Broadly tuned neurons with higher pairwise correlations to other touch neurons were more stable than neurons with lower correlations. Thus, a small population of broadly tuned and synchronously active touch neurons exhibit elevated stability and may be particularly important for downstream readout.