The growing interest for P2P overlay networks in resource sharing rises new challenges for researchers, mainly because those systems are intrinsically different from well-studied client-server environments. Finding algorithms and mechanisms to make resource sharing efficient is only the first step toward affordable, scalable and secure P2P applications. Despite the low attention put in the last years to robustness of P2P overlay networks, checking and measuring resilience of such structure with respect to faults, is a key point to push their usage in wide-range real applications. The present contribution goes into this direction, presenting an accurate study of robustness and fault-tolerance of a novel socially-inspired P2P overlay network named PROSA. We show how the self-organising structure induced by PROSA has many interesting self-adaptive capabilities, as observed in real social collaboration networks.