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We propose a distributed data replenishment mechanism for some distributed peer-to-peer-based storage systems that automates the process of maintaining a sufficient level of data redundancy to ensure the availability of data in presence of peer departures and failures. The dynamics of peers entering and leaving the network are modeled as a stochastic process. A novel analytical time-backward technique is proposed to bound the expected time for a piece of data to remain in P2P systems. Both theoretical and simulation results are in agreement, indicating that the data replenishment via random linear network coding (RLNC) outperforms other popular strategies. Specifically, we show that the expected time for a piece of data to remain in a P2P system, the longer the better, is exponential in the number of peers used to store the data for the RLNC-based strategy, while they are quadratic for other strategies.