Networks-on-Chip (NoCs) are promising fabrics to provide scalable and efficient on-chip communication for large-scale many-core systems. In place of the well-studied synchronous NoCs, the event-driven asynchronous ones have emerged as promising replacement thanks to their strong timing robustness especially when implemented in quasi-delay-insensitive (QDI) circuits. However, their fault tolerance has rarely been studied. The QDI NoCs show complicated failure scenarios and behave differently from synchronous ones. As the scaling semiconductor technology is expected with the accelerated aging process, permanent faults become more likely to happen at runtime. These faults can break the handshake, leading to physical-layer deadlocks which can spread and paralyze the whole QDI NoC. This physical-layer deadlock cannot be resolved using conventional fault-tolerant or deadlock management techniques. This paper systematically studies the impact of permanent faults on QDI NoCs, and presents novel deadlock detection and recovery techniques to handle the fault-caused physical-layer deadlock. The proposed detection technique has been implemented to protect the NoC data paths that occupy ~90% of the logic. Employing the detection and recovery techniques to protect interrouter links (~60% of the logic), a permanently faulty link is precisely located and the network function can be recovered with graceful performance degradation.