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The wide diffusion of network address translators (NATs) (and, in some respect, firewalls) may prevent some applications that require direct end-to-end connectivity (e.g. real-time media) from being able to connect to the remote party. Although the solutions currently adopted rely on centralised nodes as third party relays, the distributed connectivity service (DISCOS) architecture has been recently proposed and aims at distributing such functionalities across a peer-to-peer (P2P) overlay. The original study presented some performance characteristics of the overlay, but the ability to resist to both failures and attacks was not taken into consideration. This study illustrates the robustness feature of the DISCOS overlay and suggests some minor modifications to the original mechanisms, in order to improve the overall robustness. The key component of DISCOS is its dynamic scale-free topology. Hence, the study also extends the existing literature concerning the robustness of scale-free networks, which considers only static graphs.