This disease is named after Hans Asperger, an Austrian pediatrician. It is a milder form of autism, once a separate diagnosis but now part of a broader term called “autism spectrum disorder.” People with this condition can have high intelligence and narrow, sometimes obsessive interests but lack social skills.
Given that this disease is known by the name of a person it should be capitalized, “Asperger’s syndrome,” whereas other diseases not known by the name of a person are all lowercase.