Uncrewed aerial vehicles (UAVs) play a pivotal role in ensuring seamless connectivity for Internet of Things (IoT) devices, particularly in scenarios where conventional terrestrial networks are constrained or temporarily unavailable. However, traditional coverage-hole detection approaches, such as minimizing drive tests, are costly, time-consuming, and reliant on outdated radio-environment data, making them unsuitable for real-time applications. To address these limitations, this paper proposes a UAV-assisted framework for real-time detection and recovery of coverage holes in IoT networks. In the proposed scheme, a patrol UAV is first dispatched to identify coverage holes in regions where the operational status of terrestrial base stations (BSs) is uncertain. Once a coverage hole is detected, one or more UAVs acting as aerial BSs are deployed by a satellite or nearby operational BSs to restore connectivity. The UAV swarm is organized based on Delaunay triangulation, enabling scalable deployment and tractable analytical characterization using stochastic geometry. Moreover, a collision-avoidance mechanism grounded in multi-agent system theory ensures safe and coordinated motion among multiple UAVs. Simulation results demonstrate that the proposed framework achieves high efficiency in both coverage-hole detection and on-demand connectivity restoration while significantly reducing operational cost and time.