Neural activity maintains representations that bridge past and future events, often over many seconds. Network models can produce persistent and ramping activity, but the positive feedback that is critical for these slow dynamics can cause sensitivity to perturbations. Here we use electrophysiology and optogenetic perturbations in the mouse premotor cortex to probe the robustness of persistent neural representations during motor planning. We show that preparatory activity is remarkably robust to large-scale unilateral silencing: detailed neural dynamics that drive specific future movements were quickly and selectively restored by the network. Selectivity did not recover after bilateral silencing of the premotor cortex. Perturbations to one hemisphere are thus corrected by information from the other hemisphere. Corpus callosum bisections demonstrated that premotor cortex hemispheres can maintain preparatory activity independently. Redundancy across selectively coupled modules, as we observed in the premotor cortex, is a hallmark of robust control systems. Network models incorporating these principles show robustness that is consistent with data.