In this paper, we propose a model to improve the reliability of a mesh-based last-mile replacement for broadband connectivity in rural and underserved areas. Using open data from ten such regions, we analyze representative demand scenarios and focus on enhancing the robustness of the corresponding wireless backhaul design. We introduce graph-partitioning methodologies to construct mesh clusters with multiple gateways and increased vertex-connectivity, ensuring stronger resilience to radio and node failures. To capture the stochastic behavior of device outages, we model radio failures through a Markov-chain formulation and derive metrics such as failure probability and expected time to disconnection. Through numerical evaluation, we show that incorporating multi-gateway structures and reliability-aware topology constraints can significantly improve the resilience of rural mesh networks with only modest additional infrastructure requirements.