Have you done a forum search on here and other Expat forums for Asperger Syndrome? I have done one and found many people who have children with AS and other issues who have gained permanent residency status. I truly think it depends on the circumstances.

Does your child require a lot of care and one to one support? It seems that in cases such as these there is a little more difficulty, but residency is still possible.

I think you should seek the advice of a specialist lawyer who may be able to help.