Gary, thank you very much for your suggestion. I keep a backup of my files and was able to restore most of the presentation.
However, this does not solve my problem. I am worried about the fact that Keynote dumps most of my media without any notice. Why would the program decide to delete the majority of a presentation's assets when it claims that it has a problem to save the presentation? And why did both options - "Save anyway" or "Revert to last version" not work? I even left the presentation open over night, closed all other running programs and most background tasks but it did not help.
I am using my backups to prevent damage from mistakes I make or hard drive failures. But such a software flaw leaves me clueless. The remaining question is whether I can trust such a program.
Plus, I do not know if I can ask Apple for direct support.