This is not a surprise to me, since all this extension does is grab the URL on the image you are hovering over and passes it to SauceNAO's search. SauceNAO can search using local files, but you have to upload them using their site or use other methods. In general, any direct URL to an image that is publicly/anonymously accessible should work with the extension. This could explains the issue with some embeded images depending on the circumstance.

My extension here is meant to be very bare-bones as I made it for myself, originally, but decided to release it for others. There are more feature-rich extensions which can handle SauceNAO that may suite you better in your case.

Thank you.