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In this paper we present PEAS, a randomized energy-conservation protocol that seeks to build resilient sensor networks in the presence of frequent, unexpected node failures. PEAS extends the network lifetime by maintaining a necessary set of working nodes and turning off redundant ones, which wake up after randomized sleeping times and replace failed ones when needed. The fully localized operations of PEAS are based on each individual node's observation of its local environment but do not require per neighbor state at any node; this allows PEAS to scale to very dense node deployment. PEAS is highly robust against node failures due to its simple operations and randomized design; it also ensures asymptotic connectivity. Our simulations and analysis show that PEAS can maintain an adequate working node density in presence of as high as 38% node failures, and a roughly constant overhead of less than 1% of the total energy consumption under various deployment densities. It extends a sensor network's functioning time in linear proportional to the deployed sensor population.