This paper proposes and studies an autonomous hibernation technique and optimal hibernation policies aimed at minimizing the power consumption, while allowing stateful processing in constrained embedded systems with long-lasting lifetime requirements. To this purpose the paper models the energy contributions for hibernating the system—by saving the memory status on an external non-volatile memory and completely powering off the system—rather than maintaining the system in a sleep mode with memory retention—with problems of static leakage power—between two consecutive bursts of processing. Thanks to a simplified yet formal notion of system state, the paper rigorously determines the optimal conditions for deciding whether to hibernate or not the system during idle periods. Hibernation policies have been implemented as a module of the operating system and results demonstrate energy savings up to 50% compared to trivial hibernation approaches. Moreover, the hibernation policy proved to be robust and stable with respect to changes of the application parameters.