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Streaming live video over the Internet presents great challenges due to its sheer bandwidth requirements. Client/Server model suffers from scalability issues and high deployment cost to provide this service. Peer-to-Peer (P2P) approach provides an excellent alternative due to its potential scalability and ease of deployment. Nonetheless, a major limitation of P2P approach lies in its high dependency on users. Since peers relay content, which themselves are controlled by users, the behavior of the latter has a major impact on the streaming quality perceived by users. Indeed, unlike dedicated servers, peers join the system intermittently, which poses great challenges in providing QoS for operated live streaming services. In this paper, we propose an autonomous topology management framework for P2P live streaming architectures that minimizes the impact of peers' frequent departures. It consists in a stabilization strategy for push-based systems that moves unstable peers towards the outskirts of the topology. To validate our approach, we performed experiments on PlanetLab and show here the significant improvement of our contribution as compared to an existing system in terms of the global service quality.