Unstructured superpeer overlays are an approach to peer-to-peer systems that enables collective organization and ensures the efficient participation and use of divers peers with heterogenous capabilities and resources. Such overlays are, however, vulnerable to failures and attacks that target the superpeers in an attempt to disrupt the overlay. In this paper, we present SODAP (Self-Organized Degree Adaptation Protection), a self-organized strategy for the self-protection of the overlay, based on the local adaptation of a peer's degree in response to disconnections, whether directly detected, or indirectly discovered with the assistance of neighbor peers. When network conditions deteriorate, the SODAP mechanism induces the creation of redundant connections to superpeers, which leads to the adjustment of the entire overlay to a topology that is more resilient to disconnection, while still allowing the system to continue exploiting heterogeneous peer capabilities. When network conditions improve, SODAP responds by reducing peer degrees to reduce redundancy and streamline the topology. We demonstrate this mechanism and evaluate its effectiveness as an extension to Myconet, a self-organized superpeer overlay for unstructured peer-to-peer networks.