After several hours of frustration and searching in internet (seriously, after like 3 hours), suddenly I remember the console. Hit F12 to open Chrome console and what a surprise: an error:
Mixed Content: The site at 'https://www.amazon.es/' was loaded over a secure connection, but the file
at '**HERE COMES THE DOWNLOAD URL**' was redirected through an ...
I have this issue as well
Fix that works for me:
I read somewhere that it could be an issue relating to low battery, but this morning it happened with 54% power.
This is a good, common question that seems to have an answer here: Trouble hooking up Goodreads with sideloaded ebook on Kindle Paperwhite
I have found the best way to get it 100 percent working is this:
If your book is not already in AZW3 format then convert it. (Has to be AZW3 and not just AZW.)
Secondly, highlight the book and edit metadata.