I have a hard time believing in anything beyond the life that we currently live because people do not want death to be the end of their existence. That there could be (and I believe there is) an end to a person's existence is a scary concept and I think that it is this fear that drives so many views of the afterlife.
That being said, there is one idea that I have heard about that rings as a possibility to me. Before talking about it, I want to bring up my view of the world even before I heard about this. I have observed and experienced things that can't currently be explained scientifically (dreaming of things before they happen, having things say what I am thinking a little too often or vice versa and other 'coincidences' that seem a little too spot on.) I believe that there is a connection between all living things in their world, including through their consciousness.
The idea that I heard is that, when people die, their consciousness breaks down and pieces of it can reform with that of others to form a new one when a baby is born. Sometimes, big enough chunks can survive across from one life to the next that they can recall events from their previous lives.
Matter gets recycled within natural systems completely, along with energy that is not lost to entropy in the process. If there is the connectivity that i believe exists, it's hardly an unreasonable idea that peoples minds would be recycled in a similar fashion. Heck, maybe some of it even gets channeled into still living people, too (it would certainly give credence to how so many people think that a relatives presence is still felt even after they have died.)
As for karma reincarnations, i do not believe in them. I don't think it would be a process where people are rewarded or punished for what they did in past existences. Furthermore, Asperger's Syndrome or Autism aren't necessarily a bad thing, just different than normal. If you look around on the site, you will find a wide range of talented people, including but not limited to artists, scientists and mathematicians. In fact, there are many famous historical figures whom are suspected of having disabilities like these.
But, lets consider the possibility that you are right and not only does reincarnation happen, but it is based on a reward/punishment based system and having Asperger's indicates that you are lower on the reward spectrum than a nuerotypical person. How do you know that you are being punished after some previous human life, rather than rewarded from a previous life as an animal to join humanity (if humanity is actually considered a higher rung and not just an assumption made on human bias).