Ah, that makes sense Bjornar - browser settings. And sure enough in Firefox, turning on or off https only mode causes emojis to disappear or appear respectively.
I suspect therefore that emojis appearing and disappearing for people are linked to browser updates and the browser manufacturer changing its default settings. If you use a browser that comes as standard with an operating system, like Edge or Safari, then computer system updates may also affect the emojis.
Hope this helps everyone diagnose and fix this problem.