Thank you for the model. Does maybe a friend or neighbor have a voltmeter you could borrow? Doing electrical troubleshooting without one isn't impossible, but it's sure a challenge.
Let's approach it a different way then. When the battery appears to be dead, if you remove the spark plug will it crank over normally? You may not know the answer to this until it occurs again.
Good deal. Keep me posted. The possibilities are:
1. Defective charging system
2. Bad battery
3. Bad connection to ground
4. Short to ground
5. Valves out of adjustment
Let me know and we'll continue.