We present a fully autonomous self-recharging drone system capable of long-duration sustained operations near powerlines. The drone is equipped with a robust onboard perception and navigation system that enables it to locate powerlines and approach them for landing. A passively actuated gripping mechanism grasps the powerline cable during landing after which a control circuit regulates the magnetic field inside a split-core current transformer to provide sufficient holding force as well as battery recharging. The system is evaluated in an active outdoor three-phase powerline environment. We demonstrate multiple contiguous hours of fully autonomous uninterrupted drone operations composed of several cycles of flying, landing, recharging, and takeoff, validating the capability of extended, essentially unlimited, operational endurance.