In peer-to-peer networks for video live streaming, peers can share the forwarding load in two types of systems: unstructured and structured. In unstructured overlays, the graph structure is not well-defined, and a peer can obtain the stream from many sources. In structured overlays, the graph is organized as a tree rooted at the server and parent-child relationships are established between peers. Unstructured overlays ensure robustness and a higher degree of resilience compared to the structured ones. Indeed, they better manage the dynamics of peer participation or churn. Nodes can join and leave the system at any moment. However, they are less bandwidth efficient than structured overlays. In this work, we propose new simple distributed repair protocols for video live streaming structured systems. We show, through simulations and with real traces from Twitch, that structured systems can be very efficient and robust to failures, even for high churn and when peers have very heterogeneous upload bandwidth capabilities.