For this specific player, who already has 3 roles and 1 special ability, the only way for not having him improving his quality would be to avoid training and avoid making him play matches. Of course if he already has some "pending to apply" skill points, they will be applied tomorrow and there are chances he could increase his quality and therefore gain a new star.
This is a very specific case, and to be honest if at this point you have not been receiving direct offers for him I would sell it in the transfer market today.
The suggestion about tagging some players for not improving looks promising, I'll make sure the devs hear about it