RealFavicon Checker (which can be called from within this plugin) reports an issue with the standard favicon icon. This occurs on all sites that use RealFaviconGenerator plugin.
Error:
Image https://www.example.com/favicon.ico is ill-formed
https://www.example.com/app/uploads/fbrfg/favicon.ico and https://www.example.com/favicon.ico both exist and are different
favicon.ico is missing some icons of recommended sizes (16×16, 32×32, 48×48)
This is probably because you have an existing favicon.ico in the root of your web site. Probably from your hosting provider or WP theme.
You shouldn’t have to worry about it. The icon created by the plugin is declared in your WP pages, so your visitors will see this one, the one you create on purpose. Not the empty favicon.ico at the root of your site.
Simply said, which icon do you see when you visit your site?
@phbernard: There is no favicon.ico in site root directory though.
I can download a favicon.ico (https://www.example.com/favicon.ico) but it is just a 0-byte empty file.
The browser seems to show the favicon despite this,
sometimes it doesn’t work though and the favicon icon stays default.
Maybe that was because your site does not return genuine “404” errors, but human readable errors pages (with a “200” status). In other words, if accessing https://www.example.com/favicon.ico gives a page such as “This files does not exist” with a 200, the favicon checker thinks favicon.ico exists… but is ill-formed (of course, since HTML is returned in place of an ICO in this scenario).
If that’s the case, this is quite harmless, although genuine 404 errors are a better way to handle invalid accesses.