Behavior can be remarkably consistent, even over extended time periods, yet whether this is reflected in stable or ‘drifting’ neuronal responses to task features remains controversial. We find a persistently active ensemble of neurons in the medial prefrontal cortex (mPFC) of mice that reliably maintains trajectory-specific tuning over several weeks of performance in an olfaction-guided spatial memory task. The spatial map is stabilized during learning, upon which repeatedly active neurons show little representational drift and maintain their spatial tuning across long pauses in task exposure and across repeated changes in cue-target location pairings. These data thus suggest a ‘core ensemble’ of prefrontal neurons forming a reference frame of task-relevant space for the performance of consistent behavior over extended periods of time.