The geographic location information of a user serves as the foundation for post-disaster emergency applications. However, uncertainties in the user positioning may arise due to factors such as building obstruction and damage to ground base stations. To ensure optimal communication quality, unmanned aerial vehicles (UAVs) can be implemented to maintain close proximity to the user with a minimal turning radius. However, a small turning radius can result in increased energy consumption due to propulsion requirements. To achieve an optimal balance between high communication throughput and low energy consumption, a robust energy efficiency optimization strategy is proposed based on a fixed-wing UAV, addressing the energy efficiency of emergency communication in imprecise user locations. First, the air-to-ground channel model is established, taking into account UAV propulsion energy consumption and formulating a multi-constraint problem to maximize emergency energy efficiency. Second, by incorporating the circular region method to address location uncertainty and considering the worst-case scenario, a robust problem is formulated. Finally, the worst-case scenario is addressed by utilizing the first-order Taylor approximation and successive convex approximation (SCA) technique to solve the nonconvex problem. Through simulation experiments, the proposed scheme is compared with three benchmark schemes, demonstrating its superior energy efficiency and robustness.