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. Here, 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 while performing an olfaction-guided spatial memory task. This task-specific reference frame is stabilized during learning, upon which repeatedly active neurons show little representational drift and maintain their trajectory-specific 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.