The corona-stabilized switch has the potential to be a high repetition rate pulsed-power switching device, but there has been limited investigation into its repetitive breakdown stability and insulation recovery characteristics. Repetitive breakdowns of gas are characterized by a memory effect, where the subsequent breakdown process is inevitably influenced by the preceding one. However, there are still some issues that require further exploration in the current research on the mechanism of memory effect on repetitive breakdown characteristics. To clarify the factors and mechanisms that affect the repetitive breakdowns of corona-stabilized switches, this paper introduced optical observation methods into the experimental investigation. Through optical–electrical coupled diagnosis, the repetitive breakdown stability and insulation recovery performance of corona-stabilized switches under different working conditions and repetition frequencies were analyzed. The monotonic promoting effect of corona stabilization on switch insulation strength recovery is proposed as well as the non-monotonic and complex regulatory mechanism of corona stabilization on repetitive breakdown stability. The research results provide a theoretical and practical basis for clarifying the mechanism of repetitive corona-stabilized breakdowns and optimizing the design of corona-stabilized switches.