Make sure AE is on the latest update. Do not touch anything while it is analyzing. Sometimes the type of footage you are analyzing can cause problems. Sometimes an update on some other software can cause problems.
Without complete details it's impossible for us to know exactly what's going on.
What other details do you need to know? I'm using an mp4 file, and all updates are up to date. The file has no current edits on it- I literally just add it in and try to stabilize. The analysis goes well, then it will try to go through with step two for 2-3 seconds and I'll get the pop-up saying the program is not responding.
The problem may be your MP4 file. Try transcoding the file to a production format like QuickTime photo JPEG or maybe even an image sequence. MP4 files take a huge amount of processor power to decode and manufacture the in between frames that aren't really there. MP4 is not a very good production format.
Another problem may be the length of the shot or the movement in the frame. Warp stabilizing takes a huge amount of resources and will often fall apart if the shot is too long or there's not enough fixed geometry in the shot to complete the calculations.