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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Gaia - Why Stop With Just The Earth?
'But the stars are only atoms in larger space, and in that larger space the star-atoms could combine to form living matter, thinking matter, couldn't they?'
Microsoft VASA-1 Creates Personal Video From A Photo
'...to build up a video picture would require, say, ten million decisions every second. Mike, you're so fast I can't even think about it. But you aren't that fast.'