Players can only max in skills they have 4 or more balls in. Make sure they are not (Red) injured, if they are not injured and they still have no progress in the training report, then they are probably maxed in that skill.
Always leave a player on the skill they have just gained their 4th or higher ball in for at least one more report to make sure they have not maxed before moving them to another skill.
Another good tip is to tick the box at the bottom of the page to arrange players by number; it really does keep everything tidy.
John