I'm having the same problem.
Kubota WG750-E Walker.
Mower dies while in the middle of leaf cleanup. Yikes!
Looking it over in the shop, it gets only one spark when I try to start it,
then no more spark. Spark coil is good. Plugs are clean and gapped.
I removed the carb to get down to the distributor, and got the cap off.
My guess at this time is the spark ignitor, which is in the base of the
distributor.
My distributor is held down with some kind of a round fastener.
The ignitor is the black module near the top of the distributor base.
The two wires coming out of the ignitor go straight to the coil (which is working) so
I'm thinking it might be the ignitor.
But,
1 - how the heck do I get a tool on that round fastener, to remove the distributor?
2 - Is there some way to test the ignitor? That's a pretty expensive assembly, and
I'd like to know for sure if it's faulty.
and ..... the darn leaves are still falling!