The point-to-point key distribution technology based on twinning semiconductor superlattice devices can provide high-speed secure symmetric keys, suitable for scenarios with high security requirements such as the one-time pad cipher. However, deploying these devices and scaling them in complex scenarios, such as many-to-many communication, poses challenges. To address this, an effective solution is to build a secure key distribution network for communication by selecting trusted relays and deploying such devices between them. The larger the network, the higher the likelihood of relay node failure or attack, which can impact key distribution efficiency and potentially result in communication key leakage. To deal with the above challenges, this paper proposes an on-demand fault-tolerant routing strategy based on the secure key distribution network to improve the fault tolerance of the network while ensuring scalability and availability. The strategy selects the path with better local key status through a fault-free on-demand path discovery mechanism. To improve the reliability of the communication key, we integrate an acknowledgment-based fault detection mechanism in the communication key distribution process to locate the fault, and then identified the cause of the fault based on the Dempster–Shafer evidence theory. The identified fault is then isolated through subsequent path discovery and the key status is transferred. Simulation results demonstrate that the proposed method outperforms OSPF, the adaptive stochastic routing and the multi-path communication scheme, achieving an average 20% higher packet delivery ratio and lower corrupted key ratio, thus highlighting its reliability. Additionally, the proposed solution exhibits a relatively low local key overhead, indicating its practical value.