Are you changed the spark plug to a known good spark plug. Plugs can appear to be working outside the compression zone but fail under compression. And new doesn't always mean good either. They also fail when heated. I had several plug to this in the last five years.
I even seen ignition system to work fine off load and then a load is present fail. Just repair a Honda engine on air compressor a few weeks ago where it would run fine until the air tank was nearly full. At that time the engine would shut and not restart until I bleed the tank pressure off. I ended having to replace the ignition coil. Years ago I had a similar problem when it was just the spark going bad to do the same thing,