Insects maintain remarkable agility after incurring severe injuries or wounds. Although robots driven by rigid actuators have demonstrated agile locomotion and manipulation, most of them lack animal-like robustness against unexpected damage. Dielectric elastomer actuators (DEAs) are a class of muscle-like soft transducers that have enabled nimble aerial, terrestrial, and aquatic robotic locomotion comparable to that of rigid actuators. However, unlike muscles, DEAs suffer local dielectric breakdowns that often cause global device failure. These local defects severely limit DEA performance, lifetime, and size scalability. We developed DEAs that can endure more than 100 punctures while maintaining high bandwidth (>400 hertz) and power density (>700 watt per kilogram)-sufficient for supporting energetically expensive locomotion such as flight. We fabricated electroluminescent DEAs for visualizing electrode connectivity under actuator damage. When the DEA suffered severe dielectric breakdowns that caused device failure, we demonstrated a laser-assisted repair method for isolating the critical defects and recovering performance. These results culminate in an aerial robot that can endure critical actuator and wing damage while maintaining similar accuracy in hovering flight. Our work highlights that soft robotic systems can embody animal-like agility and resilience-a critical biomimetic capability for future robots to interact with challenging environments.