Fixed Wireless Access (FWA) networks are used to extend connectivity to areas with limited or no access, especially where the deployment of wired infrastructure is costly. In such networks, the infrastructure can take the form of a multi-hop mesh network consisting of Distribution Nodes (DNs) and Client Nodes (CNs). A CN is served by a DN and extends connectivity within homes by acting as an access point (AP). Due to fluctuations in traffic over time, network utilization also fluctuates. When the network is scarcely utilized, it leads to energy waste due to powering the network during these times. In this paper, we explore methods to reduce energy consumption in wireless mesh networks (WMNs) by implementing coordinated sleeping times for APs of the last hop and the DNs inside the FWA network. By dynamically scheduling sleep patterns in the last hop, the solution achieves network-wide energy savings without compromising the quality of service for traffic flows in terms of latency and reliability. Moreover, in this paper, we reduce the Orthogonal Frequency Division Multiple Access (OFDMA) overhead and utilize this to organize time-critical traffic in the last hop of FWA, benefiting from the coordinated sleeping time. Our results show that in medium-load scenarios, this approach can achieve up to 33% energy savings in FWA mesh networks combined with NextGen Wi-Fi while maintaining bounded latency for time-critical applications and serving non-time-critical traffic.