Thank you for testing!
Indeed, the font I use ist missing italics (there is only the standard version for free).
And no, I didn't choose the "Publisher default" font. I recently had added to the device Amazon's "bookerly" font and use it as standard, but with other fonts I had used before, such as "Georgia", the result was as you described. This evening, I'll check it out, perhaps once more with a german book to check the hyphenation behaviour again. Strange only that my font also vanishes when I add the book to the "My Digital Editions" folder and read it on the Kobo desktop.
Of your screenshots, the font appears in the first and third one, in the headings. Does it also appear in the <p> classes, that I had assigned the font to?
Edit: I just see that in the second image, the font appears as well, but only in the subheadings, not at the author's name.