Those favicons on the Bookmarks Toolbar should reappear if you click a bookmark to revisit this web page.

Did you try that?

@Cor-el - I've tried that, but unfortunately it didn't do the trick :-(

Do those favicons at least appear on the tab bar?

Did you import an HTML backup or restored a JSON backup to get those bookmarks?

Only one icon is appearing on the tab bar (the one for facebook ;-)).

I used the JSON backup to get the bookmarks

Restoring a JSON backup doesn't include the favicons, so you won't see them initially, but visiting a bookmark should make Firefox retrieve the favicon and display it.

Are favicons showing in the History?

Make sure that you do not run Firefox in (permanent) Private Browsing mode (Never Remember History).

• https://support.mozilla.org/kb/Private+Browsing

• Tools > Options > Privacy > Firefox will: "Use custom settings for history"
• Deselect: [ ] "Always use private browsing mode"

You were absolutely right - by clicking on the Bookmarks Toolbar (instead of visiting a site through another means) I was able to get many of the favicons to be displayed :-)

A few however still aren't visible (including Gmail, The NYTimes, and Accuweather), even though they are showing up in History. Any suggestions?

On a separate note, I'm not running it in Private Browsing mode

You can try to remove those bookmarks and recreate them to see if that helps. .

That's what I've been doing :-)