Due to the prevalence of peer dynamics (i.e., churn), object maintenance becomes a fundamental issue in peer-to-peer storage systems. Although quite a few prototypes have been designed and implemented, they lack theoretical analysis to shed light on how the system evolves under churn and how to configure the system properly. The performance of peer-to-peer storage systems under churn (e.g., storage capacity, bandwidth usage, bandwidth spike, etc.) also become unclear. In this paper, we develop a simple model based on stochastic differential equations, with which we can analytically study the time-evolution of peer-to-peer storage systems under churn, and the interplay between object maintenance and churn. Different from previous Markovian analysis, we provide closed-form terms to capture the time-evolution of the storage system, and formally derive its related performance metrics under different maintenance strategies. Our analytical results provide valuable directions on the optimization of peer-to-peer storage systems, e.g., reducing bandwidth usage, provisioning for bandwidth spike, improving system capacity. Besides analytical studies, our theoretical results are also validated by extensive simulations.