I have my parents set up with an Airport Base Station (router) and a Time Capsule (backup hard drive). They have big green lights on them, usually. But those turning to big annoying flashing yellow lights when there is something wrong. I happened to be at their house, so attempted to fix the issue.
By opening Airport Utility, I was able to see the problem with both: out of date firmware. Easy enough fix. The utility has a little button to click to update it.
Except, I would get this:
Of course, I web searched everywhere trying to figure it out.
The solution I figured out on my own: Just keep clicking the button and letting it fail. After 20 tries or so, it would download without error.