Any idea why my bookmarked favicon has not/will not update and how I can get it to update?

Try adding that website as a new bookmark! If you drag'n'drop a tab to the Bookmarks Toolbar, the Bookmarks Sidebar, or into one of the bookmarks drop-down menus, Firefox will save it as a new bookmark even though the same bookmark is already saved. That overrides Firefox disposition to not save a duplicate bookmark. Undocumented feature for saving bookmarks, plus the Favicon is saved immediately not on the first use of a new bookmark.

Then delete the existing saved bookmark, once you verify the new Favicon is the correct image.

Sadly that didn't work. When I dragged the tab with the new favicon, as soon as it dropped into the bookmarks toolbar it reverted to the old favicon.

Any other ideas?

The URL to that domain might be helpful. It would be nice to be able to see how the Favicon image is "set" to display in web browsers.

I am not a website creator, but back in the mid-00's I did have two personal websites where I "played with" it. Overall, the basic & original format of favicon.ico placed in the root directory of the website works best. "Hiding" the favicon image in folder (like /images/ as some people have done) could create problems, and using alternative image formats (PNG or GIF) has caused problem for web developers. https://www.w3.org/2005/10/howto-favicon

I swapped out the png for a jpg. Same problem. The favicon is on the root directory - so that's not the issue.

Bingo - thanks PKShadow!