It seems Mobi documents are now obsolete. Amazon requires one of two forms of uploading for keeping books on your Kindle. Apparently, Amazon is moving towards a more proprietary system (which should surprise no one).
There are now two ways to sideload books that you currently own (whether acquired from Amazon or elsewhere). They both use the Epub format. I’ve tested both of these methods and they seem to work reasonably well.
The first method is to upload (drag and drop) your book to your Send to Kindle page (amazon.com/sendtokindle). You need, of course, to have your own Kindle page, but this is a given if you update your Kindle anyway. It takes a few minutes, but you can watch the progress. When it goes through, the book will appear in the library on your (online) Kindle and on your own personal Kindle Digital Content page. If you any own Audible books, they also appear on this page. After your online upload, the book will remain on your Kindle, even when you go off line.
Tip: If your Epub book fails to go through, run it through a Calibre conversion Epub to Epub and the new copy should work.
The second method is to email your Epub file to yourself. I tested this once and it worked fine. Open Your account on your Kindle (Settings). At the very bottom is Send-to-Kindle email. Here you will find your own personal Kindle email address (something like xx_yyyZZ@kindle.com). Just send the Epub document/book to this address on a (blank) email and it should, after a few minutes, appear on both your Kindle and on your content page.
I haven’t tried to upload any of my own three books, so let me know (in the comments section) if this process works for them or not.
You can still sideload Mobi files directly on to your Kindle (by placing them in the documents folder). But sooner or later (most likely when you connect to Amazon) they will disappear.