Motivation. During nuclear power plant (NPP) monitoring, unmanned aerial vehicles (UAVs) can be used as an affordable and cost-efficient tool to deploy a UAV-enabled wireless network (UEWN) for providing the crisis centre (CrS) needed monitoring data from monitoring stations (MSs) of the automated radiation monitoring system in case of damage of wired networks. However, because of the high electrical power requirement, the normal operation time of a UAV of a multi-rotor type (MUAV) is just 20 to 30 min, limiting the operation time of a UEWN during NPP monitoring missions. The subject matter of the paper is the process of ensuring the persistent operation of a UEWN. The aim of this paper is to develop a queuing theory based approach to scheduling MUAVs for persistent operation of a UEWN during NPP monitoring. The objectives of the paper are: to propose a scheme of deployment of a UEWN to connect a MS with the CrS of Zaporizhzhia (ZNPP) in case of damage of the wired network between the MS and the CrS; to introduce the main parameters characterizing the automatic battery charging station (ABCS) as a multi-channel queuing system; to develop and describe in detail a queuing theory based approach to scheduling MUAVs of the UEWN for persistent NPP monitoring. The following results were obtained. A scheme of deployment of a UEWN, consisting of LoRaWAN and WiFi segments, to connect a MS with the CrS of ZNPP in case of damage of the wired network between the MS and the CrS was proposed and described. A shift schedule for 3 MUAV fleets to ensure the persistent operation of the UEWN during ZNPP post-accident monitoring missions was built. It was shown that the ABCS can be considered as a multi-channel queuing system, in which two or more channels (battery charge points at the ABCS) are available to handle arriving MUAVs. A queuing theory based approach to scheduling MUAV fleets of the UEWN for persistent NPP monitoring is developed and described in detail. It was evaluated and illustrated by means of plots how the number of occupied channels of the ABCS depends on: 1) the battery charging time for the MUAV at the ABCS, and 2) the flight distance for the MUAV between its location point in the WiFi segment and the ABCS. The next research steps can cover issues regarding to: 1) scheduling MUAV fleets for numerous UEWNs, 2) developing models of a UEWN operation using a LiFi segment for transmission of monitoring data, and 3) developing reliability/survivability models of a UEWN taking into account UAV failures or/and wireless signal interference.