This paper investigates the data persistence problem with compressive sensing (CS) in wireless sensor networks (WSNs) where the sensed readings should be temporarily stored among the entire network in a distributed manner until gathered by a mobile sink. Since there is an energy-performance tradeoff, conventional CS-based schemes only focus on reducing the energy consumption or improving the CS construction performance. In this paper, we propose an efficient Compressive Sensing based Data Persistence (CSDP) scheme to achieve the optimum balance between energy consumption and reconstruction performance. Unlike most existing CS-based schemes which require packets visiting the entire network to reach the equilibrium distribution, in our proposed scheme information exchange is only performed among neighboring nodes. Therefore, such an approach will result in a non-uniform distribution of measurements, and the CS measurement matrix depends heavily on the node degree. The CS reconstruction performance and energy consumption are analyzed. Simulation results confirm that the proposed CSDP scheme consumes the least energy and computational overheads compared with other representative schemes, while almost without sacrificing the CS reconstruction performance.