Could you post here a piece of the web part call, especially with asynch methods calls and declaration?
I was working with one case when async was enabled with Async="true" , but this created a great deal of problems. Mostly because of a way, how Kentico is handling end of requests and this caused some strange thread was being aborted exceptions.
Moreover asp.net team warns about use of asynch within web forms:
This is why it would be good to see the code of what are we dealing with.