Peer-to-peer storage systems rely on data fragmentation and distributed storage. Unreachable fragments are continuously recovered, requiring multiple fragments of data (constituting a "block") to be downloaded in parallel. Recent modeling efforts have assumed the recovery process to follow an exponential distribution, an assumption made mainly in the absence of studies characterizing the "real" distribution of the recovery process. This report aims at filling this gap through an empirical study. To that end, we implement the distributed storage protocol in the NS-2 network simulator and run a total of six experiments covering a large variety of scenarios. We show that the fragment download time follows approximately an exponential distribution. We also show that the block download time and the recovery time essentially follow a hypo-exponential distribution with many distinct phases (maximum of as many exponentials). We use expectation maximization and least square estimation algorithms to fit the empirical distributions. We also provide a good approximation of the number of phases of the hypo-exponential distribution that applies in all scenarios considered. Last, we test the goodness of our fits using statistical (Kolmogorov-Smirnov test) and graphical methods.