In this paper, we propose and study analytical models of self-repairing peer-to-peer storage systems subject to failures. The failures correspond to the simultaneous loss of multiple data blocks due to the definitive loss of a peer (or following a disk crash). In the system we consider that such failures happen continuously, hence the necessity of a self-repairing mechanism (data are written once for ever). We show that, whereas stochastic models of independent failures similar to those found in the literature give a correct approximation of the average behavior of real systems, they fail to capture their variations (e.g. in bandwidth needs). We propose to solve this problem using a new stochastic model based on a fluid approximation and we give a characterization of the behavior of the system according to this model (expectation and standard deviation). This new model is validated using comparisons between its theoretical behavior and computer simulations.