My son AND me got SSDI. Let me tell you what I was told.
They NEVER ok it the first time. Or the second. Or the third. It goes to a different person each time and not until the FOURTH try does it go to the RIGHT person. They are hoping you will quit trying. Do not quit trying. Apply again. Keep applying. Make sure you attach all the medical records you have. And if they turn you down the fourth time, then you can get a lawyer, but this is the way SSDI is done. It is the same for everyone, kids or adults. KEEP AT IT. He will eventually be accepted, but you have to stay the course.
Also certain key words help. "Autistic spectrum disorder" "cognitive delays not otherwise specified" "bipolar disorder"...they help a lot more than "ADHD" "ODD" "Conduct Disorder", "Sensory Integration Disorder" etc. What is his legal diagnosis. by the way, a cognitive delay can be many things. It does not have to mean he has a low IQ. On the Asperger's front, it is better if he is diagnosed with autistic spectrum disorder (my neuropsychologist knew to do that to son) although he is very high functioning. They need to think it is a lifelong disorder.
I would not appeal it. I would re-apply. Wait for the fourth time to do anything.