Wireless Multi-hop Infrastructures (WMIs) enable mobile users to access the Internet through wireless multi-hop connections. Compared with conventional network infrastructures, WMIs have the low cost and flexible network deployment. The applications of WMI include smart cities, emergency responses and Internet of things. In emergency situations, WMI networks may have energy constraint. Furthermore, user mobility may be restricted to a limited area. In this paper, we study the network sustainability performance in WMI networks that have energy constraint and limited scope of user mobility. The sustainability of the WMI depends on network energy, connectivity, as well as user distributions. The collective sharing of network tasks among infrastructure nodes highly affects the network sustainability. However, few studies to date addressed the sustainability performance of network with the decreasing of both node energy and network connectivity. This paper specially examines the impact of decreasing energy and connectivity depletion in WMIs that have biased scope of user mobility. Performance evaluation is conducted based on packetlevel simulations. The evaluation show spatio-temporal features of energy-and-connectivity in WMI networks. With the investigation of various routing metrics, evaluation results show that energyaware metric leads to the collective sharing of packet forwarding with 16-30 percent improvement at the BSs out of the user mobility scope. The results also show that limited scope of user mobility leads to a decrease of network lifetime.