In industrial millimeter-wave (mmWave) multi-hop Integrated Access and Backhaul (IAB) networks, dynamic blockages caused by moving obstacles pose a severe threat to robust and continuous networks. While Packet Duplication (PD) enhances reliability by path diversity, it inevitably doubles the traffic load, leading to severe congestion and degraded Age of Information (AoI). To navigate this reliability-congestion trade-off, we formulated an optimization problem in a multi-hop IAB scenario that minimizes the average AOI while satisfying strict queue stability constraints. We utilize Lyapunov optimization to transform the long-term stochastic optimization problem into tractable deterministic sub-problems. To solve these sub-problems efficiently, we propose a Resilient and Freshness-Aware Scheduling (RFAS) algorithm. Simulation results show that in blockage-prone environments, RFAS significantly outperforms baselines by maintaining a Packet Delivery Ratio (PDR) above 95\%. Crucially, it strictly guarantees queue stability under hard buffer constraints, whereas baselines suffer from buffer overflows. Furthermore, RFAS reduces the network load imbalance by 19\% compared to the baseline in high-frequency traffic scenarios. This confirms RFAS as a robust and sustainable solution for real-time industrial control loops.

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