Neural activity maintains representations of information that bridge past and future events, often over many seconds. We used optical and electrophysiological methods to probe the circuit mechanisms underlying short-term memory in the mouse premotor cortex. We find that persistent activity is remarkably robust to large-scale transient perturbations. These persistent representations are distributed across interacting neural circuit modules, a hallmark of robust control systems. Network models incorporating modularity show robustness that is consistent with data.