Everythings looks ok in the preview but turns out to be messed up in the online website. It sometimes looses Google fonts in the startup but gives no indication. (Btw the webfonts are in the same folder as the project.) I also have the impression that the program then kicks the reference to the fonts so it recovers to the basic used font.
It seems that Website X5 sees that it has to use the font, but doesn't link it to the fonts location, thus missing the font in the project. I encounter this problem in Website X5 v15 and v16. I select these fonts again and after uploading it seems that for the uploaded webfont, Website X5 creates a new upload with the number 1 selected.
Sometimes 1 uploaded Webfont and 1 selected Google Font is missing, or both or more Google fonts.