The Saturnian satellite Enceladus is enigmatic in that its geologically active south polar region shows high heat flows1 and geysers 2 not seen elsewhere on the satellite at present; its heavily deformed surface shows an episodic age distribution2; and the current observed heat loss exceeds the long-term tidal equilibrium heat production by a factor of at least 3.5 (ref.3). These observations, which are not explained by existing convection models for Enceladus, suggest episodically active tectonism4,5. Here we present scaled numerical convection models of Enceladuss ice mantle, and show that all three observations are explained if convection is in a regime that involves occasional catastrophic overturns lasting about 10 million years, during which portions of the rigid ice lid are recycled into the interior, causing transiently enhanced heat loss. Our models show that episodic partial lid recycling occurs for plausible lid strengths and Enceladuss estimated supply of tidal energy. The localized nature of such overturn episodes, their periodicity of 0.1-1 billion years and an anomalous heat flow during these episodes are consistent with Enceladuss geology and heat supply. We propose that localized catastrophic overturn events may also explain the episodic partial resurfacing that has been inferred for other satellites, such as Ganymede, Rhea and Miranda.