I know you say it always has spark but it sure sounds like it is losing spark! Wet plug, won't start after a run, etc. Just for yucks, did you try another spark plug? If it were me, I would put my highly visible timing light on the plug wire, verify that it is flashing well when the engine is running, then observe it when the engine won't start. If it doesn't flash, either the plug is fouled or there is, in fact, no spark. However, given the fact that it's a Jap motor, the chance of its having no spark is slim to none.
As I write this, it also occurs to me that if the plug is wet with good spark, maybe is is flooding somehow when left to sit, like a weeping float valve or hole in a fuel pump diaphragm?