My SD card (that came with the Cybook) died. The Cybook suddenly didn't recognize it and the computer told me the card had to be reformatted, but wasn't able to do so.
I started using another SD card that I had lying around and suddenly all my bookmark problems disappeared.

Now bookmarks work perfectly and the Cybook always remembers where I left off. I'm crossing my fingers that everything will work fine from now on. But I will bring a backup SD card with books on when I go on holiday next month.