WHAT AM I DOING WRONG?
I'm running the trial of After Effects version 18.104.22.168
Sorry, but CC 2015 is a neverending nightmare. Downgrade to CC 2014.
I just tried the same steps in AE CC 2014 - SAME PROBLEM! Somehow, I'm getting the exact same error, at the exact same 35% complete point during analyzing.
The first thing I would suspect is the footage. Some footage won't warp stabilize. Some video codecs or formats are not friendly to stabilization. If you're trying to stabilize very long clip you can also run into problems. The first thing I would try is stabilizing another clip with another video format. If that works it's probably not your system, it's probably the footage. Try trimming it so it is shorter. Try rendering to a good intermediate codec that is frame based or render the footage to an image sequence. Let us know how it goes.