Yes - the kill wire is the magneto grounding wire. The ignition coil (the device at the other end of the spark plug wire) is suspect if your engine dies after several minutes. They can develop faulty insulation which fails when hot.
Re: updates - just post an 'answer' to your original question. I review all questions I answer periodically to see if the orignal poster has added any info.
phil_saunders@bigfoot.com
Phil Saunders, September 2008