Although unmanned vehicle fleets offer efficiency in transportation, logistics and inspection, their susceptibility to failures poses a significant challenge to mission continuity. We study the Multi-Depot Rural Postman Problem with Rechargeable and Reusable Vehicles (MD-RPP-RRV) with vehicle failures, where unmanned rechargeable vehicles placed at multiple depots with capacity constraints may fail while serving arc-based demands. To address unexpected vehicle breakdowns during operation, we propose a two-stage real-time rescheduling framework. First, a centralized auction quickly generates a feasible rescheduling solution; for this stage, we derive a theoretical additive bound that establishes an analytical guarantee on the worst-case rescheduling penalty. Second, a peer auction refines this baseline through a problem-specific magnetic field router for local schedule repair, utilizing parameters calibrated via sensitivity analysis to ensure controlled computational growth. We benchmark this approach against a simulated annealing metaheuristic to evaluate solution quality and execution speed. Experimental results on 257 diverse failure scenarios demonstrate that the framework achieves an average runtime reduction of over 95\% relative to the metaheuristic baseline, cutting rescheduling times from hours to seconds while maintaining high solution quality. The two-stage framework excels on large-scale instances, surpassing the centralized auction in nearly 80\% of scenarios with an average solution improvement exceeding 12\%. Moreover, it outperforms the simulated annealing mean and best results in 59\% and 28\% of scenarios, respectively, offering the robust speed-quality trade-off required for real-time mission continuity.