I left the reader on this morning, playing music at full volume, while connected to the solar charger. It was collecting about 12-20mA from the charger, nevertheless the battery display went from 4 to 2. So I turned the reader off (including pause of the music player) and left it connected to the charger. Later when the sun showed itself the current went up to 60mA, however after several hours the battery indicator did not move.
Well, it looks like either you use the solar panel in full sun-light (maybe that's why it is called solar-panel and not light-panel) or you need a much bigger surface.
At this point I am not going to beat the horse any longer and will just carry a usb cable with me when the battery starts getting low.