This paper considers a large-scale wireless sensor network where sensor readings are occasionally collected by a mobile sink, and sensor nodes are responsible for temporarily storing their own readings in an energy-efficient and storage efficient way. Existing data persistence schemes based on erasure codes do not utilize the correlation between sensor data, and their decoding ratio is always larger than one. Motivated by the emerging compressive sensing theory, we propose compressive data persistence which simultaneously achieves data compression and data persistence. In the development of compressive data persistence scheme, we design a distributed compressive sensing encoding approach based on Metropolis-Hastings random walk. When the maximum step of random walk is 400, our proposed scheme can achieve a decoding ratio of 0.36 for 10%-sparse data. We also compare our scheme with a state-of-the-art Fountain code based scheme. Simulation shows that our scheme can significantly reduce the decoding ratio by up to 63%.