Small Engines (Lawn Mowers, etc.): Kohler 301, spark problem, spark plug wire, spark tester

Question
I have a Jacobsen mower with a Kohler 301AQS engine (battery, electric starter and points ignition system).  I am having problems getting it running.  Using a spark tester, there is no spark to an erradic spark.  The keyswitch was bad, so I have replaced that.  I also replaced the coil, condenser, breaker points and spark plug.  There is good continuity with the spark plug wire, though it was not replaced.  There is a full 12 volts getting to the (+) terminal on the coil.  The condenser is grounded well.  Gap of the spark plug and breaker points are good.

At one point this morning, I had it running for about 15 seconds, then it died and again no spark was found when tested.

Any suggestions where the problem could exist?

Answer
Hiya David-
At this point I suspect a problem with the ground part of your electrical system.  Check your battery ground connection very closely.  Also the ground wire from the coil.

If this is ok- monitor the 12v supply to the coil during the problem.  Sounds like a poor connection- you just gotta find it-
lemme know what you find!