The challenge is that there are two different "stages" I'm learning about among autistic individuals. As children, many high-functioning autistics seem to deal better with adults. As adults, the opposite seems to be the case, with autistics relating better to children. The challenges make sense, though, as I will explain.
As a child, the individual with Asperger's or any "high-functioning" ASD diagnosis is likely drawn to concrete thinking, pattern recognition, and might be an "expert" on a few subjects of special interest. Compared to his or her peers, the autistic seems "advanced" because some skills we associate with greater chronological ages appear early. These are not social skills, however.
The interest in topics and things, compared to other children's interest in play and socializing, appears "more mature" at first. This same situation occurs among gifted children, so a "twice special" child is going to be particularly prone to this "things not people" period of development.
Other children are unlikely to care about a single topic as intensely as the autistic, while adults view the specialization as an impressive sign of intelligence. Even when a splinter skill is not a sign of innate reasoning or analytical skills, adults only notice the skill or memorization is advanced beyond that of "normal" children. The autistic finds adults will indulge a special interest, especially in a young child. Adults become the safe, supportive audience for some time.
By adolescence the special skills and concrete reasoning of many autistics no longer entertains adults. The adults have become tired of hearing about anime, Disney films, space exploration, weather data, or other narrow interests. It's also no longer possible to ignore that the special interest or splinter skill is not linked to abstraction. The advanced cognitive abilities of analysis, synthesis, and evaluation likely trails the abilities of peers.
So, the autistic once rejected by children find herself or himself alienated from many adults over the years. By the late teen or early adult years, I've witnessed many autistics seeking out children as friends. The social skills he or she lacked as a child might now be in place, years later than is "typical" for development. The autistic can now relate to children — and recognizes that adults are less and less available.
Imagine being accepted by adults until your teen years, only to feel rejected as an adult. Yet, the young children who would have rejected you as a peer become more and more approachable as you learn social skills. It is as if your social circles went "backwards" from adults to children, while everyone else moved in the opposite direction.
When asked for advice on this social alienation, I generally suggest social groups and safe social settings.
Depending on the needs of your child (or yourself) you might find groups that are dedicated to autism, ADD/ADHD, and other socially frustrating challenges. I've also found groups of "gifted" people include many members with ASD and ADHD traits. You can also join groups dedicated to a special interest, from birdwatching to trains. These groups are good because being a specialist is embraced and celebrated. Social skills are secondary to the shared interests and experiences of members in these various organizations.
I have few close friends, and I know I can seem "odd" to other people. At some point in life, you accept being different is okay.