It may be the connection (solder joints). LEDs generally don't burn out--they fade in brightness over time. It's accelerated by heat and humidity.
I swapped keyboards around again, and now that the Ducky is on my Mac the Caps Lock light is working again!
The KeyCool which was on the Mac with the Caps Lock light working is now connected to my server (Ubuntu in text mode) and Caps Lock on that does not work.
So I suspect it is just something Linux is doing, or not doing, that is preventing the LED from lighting.