In this paper, we propose a failure recovery protocol named QuickSwap for mesh-based P2P live streaming systems. Unlike the existing mCache-based failure recovery scheme, QuickSwap enables peers to quickly recover their live streaming quality from neighbor failures by exchanging and pre-processing of local streaming information. Our contributions in this work are two-fold. First, QuickSwap's lightweight streaming-information exchange protocol together with the proposed neighbor maintenance and streaming-quality estimation methods provide a significant performance edge over the conventional mCache-based failure recovery. Second, we have built a system model for our proposal and have evaluated QuickSwap's performance under different system settings through simulation methodology. Our results reveal that at a small, affordable overhead cost, QuickSwap protocol can support fast recovery of live streaming quality with a nearly 100% failure recovery success rate and a fail-over time less than one second for an average of exponentially distributed peer lifetimes as low as 10 minutes.