There are several reasons we could think of, though I’m sure there could be others asd well.
1) The site could be using the Content-Security-Policy header. It’s possible that could block one of the scripts from loading. I think this would be listed in your browser developer tools Console tab if that is the case. We have a guide below:
https://www.wordfence.com/help/advanced/troubleshooting/#how-to-inspect-the-browser-developer-tools-console
2) Previous bad cache settings on the site could mean you are still getting the old JavaScript and it’s failing to load. it may show up as a 404 or 403 response status code in your browser developer tools Network tab.
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3) A browser extension could also prevent the logo from loading. This should be visible in the Network tab.
4) Google might possibly consider your IP address to belong to China as people have had problems before with Chinese IP addresses accessing Google reCAPTCHA servers.
The important thing to note is that no matter if the logo shows or not, it doesn’t affect the reCaptcha functionality.
Tim