In avionics system networking, mixed‐critical networks are commonly used to integrate system applications with different levels of guarantees for various traffic classes on a shared resource platform, effectively addressing issues such as cabling, cost, weight, volume, power consumption, etc. However, current fault recovery and reconfiguration techniques mainly focus on high‐priority time‐triggered (TT) traffic, often neglecting the impact of TT traffic reconfiguration on low‐priority traffic. This paper proposes an avionics mixed‐critical networking approach based on the IEEE 802.1CB protocol, which is shown to be more effective for the post‐failure recovery of Rate‐Constrained (RC) traffic (a typical type of low‐priority traffic in TT networks). Furthermore, an elastic reconfiguration algorithm is presented to ensure quality of service for RC traffic during and after reconfiguration, preventing arbitrary application and traffic shutdown triggered by TT traffic reconfiguration. Simulations demonstrate that the proposed approach and algorithm can significantly improve the post‐failure recovery ratio of RC traffic, as well as guarantee quality of service and network throughput of RC traffic during and after reconfiguration to a certain extent.