Persistent neural activity in the absence of a stimulus has been identified as a neural correlate of working memory, but how such activity is maintained by neocortical circuits remains unknown. We used a computational approach to show that the inhibitory and excitatory microcircuitry of neocortical memory-storing regions is sufficient to implement a corrective feedback mechanism that enables persistent activity to be maintained stably for prolonged durations. When recurrent excitatory and inhibitory inputs to memory neurons were balanced in strength and offset in time, drifts in activity triggered a corrective signal that counteracted memory decay. Circuits containing this mechanism temporally integrated their inputs, generated the irregular neural firing observed during persistent activity and were robust against common perturbations that severely disrupted previous models of short-term memory storage. These results reveal a mechanism for the accumulation and storage of memories in neocortical circuits based on principles of corrective negative feedback that are widely used in engineering applications.