Adobe PDF will not save rotated pages...why?

It’s usually because Acrobat is just changing the View rather than the actual page attributes. If you're just hitting the rotate button in the top toolbar, it doesn't always 'stick' when you save. You usually have to go into 'Organize Pages' and rotate them there to make it permanent.
If the file permissions are being weird and won't let you save the changes in Acrobat, I’ve had luck using this quick web tool- https://www.thetoolapp.com/rotate-pdf-pages/. It’s much faster than troubleshooting the Adobe settings when you’re in a rush.

Adobe respects the PDF specifications (which it created), which is not necessarily the case for other programmers.
If Blurb.com's machines don't recognise the rotation of a page, the problem is probably theirs.

This is a Blurb.com issue, you should ask them about.

Carlisle1500,  watching your video again, I realise that it's the interface of the new Acrobat that's confusing.
In the video you're using the "Rotate View" tool, but the tooltip says "Rotate Document", which is a design error.
In fact, after using this tool on a document that has just been saved, you can see that the "Save" menu item remains greyed out, which means that it is indeed a "Rotate View" because it doesn't modify the document.
If it were a 'Rotate Page', this would not be the case and the Save item would be enabled.

Amal., I think you should report this issue to the development team as soon as possible.

The video:

The tooltip:

The greyed out Save menu item after using this tool:

Don't confuse "rotate view", which has always been available in Acrobat Reader, Acrobat Pro and Acrobat Standard to prevent the reader from having to tilt their head or their screen WITHOUT modifying the document, with "rotate page", which has never been available in Acrobat Reader (only in Acrobat Pro and Standard) and which is used to modify the document.

In both cases, you can apply the rotation to several pages at once, depending on the selection.

This is because you're not rotating the page, you're rotating the view.

[Edited response]

Hi @Carlisle1500 

I hope this message finds you well, and I appreciate you bringing this matter to our attention.

As correctly mentioned by JR Boulay

You will find success by rotating the page through the following steps: navigate to Tools > Organize Pages, adjust the page orientation as needed, then save the PDF file.

Got your issue resolved? Please label the response as 'Correct Answer' to help your fellow community members find a solution to similar problems.

~Amal