Recent long-term measurements of neuronal activity have revealed that, despite stability in large-scale topographic maps, the tuning properties of individual cortical neurons can undergo substantial reformatting over days. To shed light on this apparent contradiction, we captured the sound response dynamics of auditory cortical neurons using repeated 2-photon calcium imaging in awake mice. We measured sound-evoked responses to a set of pure tone and complex sound stimuli in more than 20,000 auditory cortex neurons over several days. We found that a substantial fraction of neurons dropped in and out of the population response. We modeled these dynamics as a simple discrete-time Markov chain, capturing the continuous changes in responsiveness observed during stable behavioral and environmental conditions. Although only a minority of neurons were driven by the sound stimuli at a given time point, the model predicts that most cells would at least transiently become responsive within 100 days. We observe that, despite single-neuron volatility, the population-level representation of sound frequency was stably maintained, demonstrating the dynamic equilibrium underlying the tonotopic map. Our results show that sensory maps are maintained by shifting subpopulations of neurons "sharing" the job of creating a sensory representation.