I meant the region in “Manage Your Content and Devices” > Country/Region Settings. This has to be set to Japan, otherwise it won’t work in my experience. I’ve once suggested this to another poster on this forum and it fixed their issue.
But as the others said, I can’t rule out completely that you don’t need to be in Japan (virtually or for real) every once in a while for this to keep working.
And once you have the Kindle books, the first thing I usually do is extract them to text using Calibre (you need an old version of the Kindle Cloud reader installed, won’t work with newer versions). Then I paste this text in japanese.io (my favorite way of reading at the moment) or use an iOS app called Wakaru to read the content. I’m quite disappointed with the Kindle built in dictionary lookup.