Unmanned Aerial Vehicles (UAVs) communications attracted significant research interest in recent years as a promising tool for future wireless communication systems (beyond fifth-generation (B5G)/sixth-generation (6G)) due to their numerous capabilities and broad applicability. In this paper we consider a UAV-enabled wireless communication system consisting of two ground base stations. Owing to distance, direct communication is not feasible for the ground stations. For this reason a UAV is used to travel periodically between the ground stations in order to enable communication. This communication model is widely used in single UAV architectures enabling throughput maximization and increased network security (especially in military applications). Since the performance of this communication system depends on several factors, in this paper we examine the Age of Information (AoI) performance of the system under different parameters, such as the number of packets exchanged between the ground base stations, the distance between the ground stations, the frequency that each ground station receives data packets and the SNR level since transmissions take place via an error-prone channel. Furthermore, we derive an analytical expression for the AoI considering the aforementioned parameters, and finally we provide simulation results that illustrate the impact of the network operating parameters on the age performance, considering the trade-off between the amount of data transferred through the network and the freshness of data exchanged between the terrestrial base stations.