The Special Skill increase isn't guaranteed on every level up. When levelling up your Hero, the "Special Level Up Chance" shows you how likely it is to increase the level of the Special Skill.

You can increase your chances by training the Hero with multiple heroes of the same colour and even more by training with a duplicate Hero.

Please also note that ascending a Hero increases the level of Special Skill by 1 automatically if the skill level is not yet maxed.