Whenever ive read about the s3 "forgetting" things, its been caused by people not factory resetting after updating to jellybean. Sounds like you had the problems with ICS though.
Have you tried the app Default Manager?

 

I am having this problem. My S3 forgets every default, even asking if I want to use the phone or Skype every time. Forgetting the launcher is the worst. I tried Default Manager but once I set it, it quickly forgets. No more Samsung for me...