@bronek, do you by chance have anything stuck in indexing? From main menu, search for a gibberish, e.g. "asdfasdas", an then select "Book still indexing (n)" (or something like this in the bottom, can't remember. "n" is the number of books being indexed). It will show you books which are "still being indexed". If that's the case, than try to remove the book(s) and restart. If it helps, then a) probably the book(s) is (are) bad for Kindle with some weird formatting or too large PDF scan pages; or b) you could try to re-upload them to Kindle and see if it helps.
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