yes that is when it happens, it breaks down just as you pass Cosmo Canyon, if you get out and go into the canyon before ever reaching it then there is no need for it to break down as you're entering a new storyline part the moment you climb those stairs... i wonder if it will break down if you try to leave before going through the Gi Cave, i never tried leaving since the buggy always breaks down on me, i like to park in front of the towns enterances...