I have no idea if there is a cap or not. Your best bet is to talk to someone directly in the Social Security Administration itself. Their publication that deals with this issue is:
"Benefits for Children with Disabilities:
http://www.ssa.gov/pubs/10026.html
order Pamphlet 05-10026"
Unfortunately, this publication does not describe a max parental income for the child to be able to receive benefits, just for Supplemental SS Income the child has to come from a "needy family" but "needy" is not defined either. This information likely comes from state guidelines due to variations in how far the parents income goes (cost of living) in NY compared to other states.
I am disabled, too, and when I was taking therapy from Easter Seals therapists instructed, had physical, occupational, speech therapy for many physically handicapped and/or developmentally delayed pre-schoolers and a lot of them received benefits and quite a few were from middle class families. If there's an Easter Seals in NY you can check with them to see if they have any ideas. It helps to have an trained "advocate" - certain folks just know how to navigate the "system" better than me.
Go to SSA.gov if you haven't done so already; it's an excellent site and contains links to programs for children with disabilities. This site also contains links specifically to NY resources (advocates as well as other helpul resources).
My very best wishes for you and your child.
