Sandia National Labs and Northrup Grumman have been working on nuclear drones that could stay up for months at a time. NASA has even been given a proposal for a nuclear powered drone mission to Titan.
(Dragonfly nuclear drone mission to Titan)
The idea is that a nuclear-powered drone could not only stay up for a very long time, but could carry more payload, varied weapons and stay on station for longer.
As I recall, the eyes, world-spanning drones from Roger Zelazny's 1966 story This Moment of Storm must have used some sort of very long lasting power source, since they stayed up almost indefinitely. Just the thing for one person to use to monitor an entire planet.
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LLM 'Cognitive Core' Now Evolving
'Their only check on the growth and development of Vulcan 3 lay in two clues: the amount of rock thrown up to the surface... and the amount of the raw materials and tools and parts which the computer requested.'