I know this thread is a little old, but thought I'd throw in my findings having had the same issue with my PaperWhite 7th generation Kindle - and think I found the solution.
A while back I'd been connecting my PaperWhite to my HUB 4 without problems. I recently attempted to connect to the WiFi but no evidence of my router on the Kindle WiFi networks. "Somewhere" on here, someone mentioned setting the 2.4 GHz channel to between 1 & 11 (NO HIGHER !!). Bingo .... I remembered I'd set mine to channel 14 due to our neighbours darn Sky multi WiFi transmissions all over the place.
I set the 2.4 GHz channel to 11 (the quietest channel available when I used WiFi Analyzer app to check). Voiala - PaperWhite suddenly saw & connected to WiFi. As a test, I changed the channel to 12, 13, and 14 ... all failed to be seen.
So, login to your router on 192.168.0.1
Go to Advanced settings / Wireless signal / Set Channel to "MANUAL" / choose a channel between 1 and 11 / Apply changes.
Wait a minute or so for settings to save then refresh WiFi on your Kindle, and hopefully you'll see your Routers SSID.
Hope this might help and fix anyone else with the issue. Thanks to "whoever" mentioned channel 11 being maximum number to select. I can't immediately find the page again 👍
