I hope you can figure out what is getting your chickens, and how to defeat it! I think it more than likely was the owl (s)
Here is a little constructive criticism ... on your fence ... I think if you could at a very minumum pull the tops of the corner T-posts in, and securely brace them to the wooden posts, then you can pull/stretch the hot wire tight and straight.
Better yet, the T-posts will bend some, I would also get the ground wet, and take a 8-10 pound sledge hammer, and drive the base over closer to the wooden posts, even only an inch would help, then pound a rock in the gap you created in the dirt/ground.
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I really doubt that a critter would be able to "learn" that only a few wires were full power "hot" ... and to step over them while climbing ... one zap, and they don't usually try a second time!
I also doubt that a critter was able to get around or through the hot wires three nights, without getting zapped! Even with fur as an insulator, not likely it would be so lucky to miss all the wires, on multiple nights.
While a cat may have been able to jump over the whole fence, clearing it in a single bound, most critters will first checkout the fence with their nose ... and would have been zapped, and would in the future give a very wide berth to the fence.