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Node churn and failures exist as fundamental characteristics in both peer-to-peer (P2P) and sensor networks. Peers in P2P networks are highly dynamic, whereas sensors are not dependable. As such, maintaining the persistence of periodically measured data in a scalable fashion has become a critical challenge in such systems, without the use of centralized servers. To better cope with node dynamics and failures, we propose priority random linear codes (RLCs), as well as their affiliated predistribution protocols, to maintain measurement data in different priorities, such that critical data have a higher opportunity to survive node failures than data of less importance. A salient feature of priority RLCs is the ability to partially recover more important subsets of the original data with higher priorities, when it is not feasible to recover all of them due to node dynamics. We present extensive analytical and experimental results to show the effectiveness of priority RLCs.