As a 40 year old CAH male (non-salt wasting) who’s been taking either prednisone or hydrocortisone for 36 years in varying doses and frequencies, let me say that I feel better during the day when I "kick start" the morning with a larger dose.  I like to hit the ground running.  I have also always been tested on a regular basis to make certain I know how my body is reacting. 

Your doctors may be right about what goes on in the body during the night, but do not discount how your child feels.  With infants, this is obviously a challenge, but as soon as they can communicate, ask them.  Teaching a child to share how they feel can benefit them in many ways down the road, as well.

Hope this helps.  Best, Eric