I don't have a Cybook, so what suggestions I can offer are pretty limited. One thing does occur to me to try which you haven't mentioned doing (though you may have tried it and just not mentioned). You might try charging it fully -- I mean connecting it up to charge and leaving it until the charge light goes out (Cybooks have a charge light, don't they?
).
What you're seeing happens to Sony devices when they get totally flat, and sometimes the battery meter will still show a partial charge. Like I say, I have no idea if it'll help, but it's not likely to hurt anything, so ....