Breakdown of a dielectric material at high electric fields significantly limits the applicability of metal-dielectric-metal capacitors for energy storage applications. Here we demonstrate that the insulating properties of atomic-layer-deposited Al2O3 thin films in Al/Al2O3/Al trilayers can recover after the breakdown. The recovery has been observed in samples with the dielectric thickness spanning from 4 to 9 nm. This phenomenon holds promise for a new generation of capacitors capable of restoring their properties after the dielectric breakdown. Also, if employed in capacitor banks, the recovery process will ensure that the bank remains operational even if a breakdown occurs.