The way the book works now is that it gives an amount of skill proportional to the number of kills the "writer" of the book got during the round. It seems though that often the amount of skill you get is less than 1 (meaning it's just progress towards the next whole skill level), in which case there's no notification about the skill increase.
It also seems that the amount of kills you need to get any meaningful skill increase seems to be pretty high now. We'll look into improving this, sorry for the inconvenience!