KZ400 shutting off

I have an '81 KZ440 with ~16.5k miles.
Recently it has started to sometimes shut off on me when coming to a stop/idling, I generally can restart the bike by bump starting it. The starter does spin the motor when this happens, but it doesn't even try to start.

I've checked my battery and it is fine, it's charging how it should when the bike is running. The carbs have been cleaned and jetting is completely stock. The valves are in spec. The coils are ~2 year old Dyna 3 ohm coils, which were producing good spark when I checked.

This isn't a problem I can recreate, so I don't necessarily know how to test any fixes.

Any ideas?

Can it be unstable/bad/poor connection some where?

Have you checked the fuses for poor connection?

My fuses are good and solid, I'll go around the bike and make sure all of the connectors are snug.

It's an odd situation, and it's frustrating me to no end.