WIthout proper system info, exact version info, comp settings, drive configuration etc. Nobody can even guess.
I have the exact same problem on a Late 2013 Mac Pro, 6-core with 32GB of Ram running the latest Mavericks.
It's incredibly frustrating since no one from Adobe will even talk about this in any thread.
ALSO EXACTLY the same problem. Autosave kicks in (even when switched off) during stabilisation process and freezes AF.
Trying to solve it for a week now. Nothing has worked. I have had to do the stabilisation work on my Mac laptop(no issue there) instead of my new MacPro late 2013 model, OS 10.1, 64 GB Ram, FirePro D700 graphics. AF 13.1.1 Very frustrating.
I have switched off autosave in preferences, re-installed AF, given more RAM to secondary apps, trashed preferences... same result.
I don't know what to try next? I would love to know if anyone has solved this problem.