Electrically deformable surfaces based on dielectric elastomers have recently demonstrated controllable microscale roughness, ease of operation, fast response, and possibilities for programmable control. Potential applications include marine anti-biofouling, dynamic pattern generation, and voltage-controlled smart windows. Most of these systems, however, exhibit limited durability due to irreversible dielectric breakdown. Lowering device voltage to avoid this issue is hindered by an inadequate understanding of the electrically-induced wrinkling deformation as a function of the deformable elastic film thickness. Here we report responsive surfaces that overcome these shortcomings: we achieve fault-tolerant behavior based on the ability to self-insulate breakdown faults, and we enhance fundamental understanding of the system by quantifying the critical field necessary to induce wrinkles in films of different thickness and comparing to analytical models. We also observe new capabilities of these responsive surfaces, such as field amplification near local breakdown sites, which enable actuation and wrinkle pattern formation at lower applied voltages. We demonstrate the wide applicability of our responsive, fault-tolerant films by using our system for adjustable transparency films, tunable diffraction gratings, and a dynamic surface template/factory from which various static micropatterns can be molded on demand.