[bestgenman]

Robert, there are several items to check.  First let me explain the operation of the solenoid.  There are two coils inside, one for pull in and the other for hold in.  On most Kohler sets, the pull in is tied to the starter motor.  The pull in has quite a bit of strength and draws a lot of current so, it can’t stay energized long or else it will fail.  After the iron core is pulled inside, the hold in keeps it in.

My first reading of your problem leads me to think the iron core and the inside of the coil housing is dirty so first, I would clean and lube with dry graphite or molybdenum disulfide.  It needs to slide freely.  Check linkage adjustment to be sure the core will bottom out inside the coil housing and not be stopped by the end limit of the injector pump lever stop.

The hold in ,as someone mentioned, is in series with a pressure switch on the fire extinguisher.  Be sure that switch is closed and there is power on the hold in circuit.   If there is no power on the hold in, as someone said, check the fuse and for corrosion of connections.   Also, if your generator is not making voltage, the control circuit will not power the hold in.   The hold in power is the same as the lift pump power.   And finally, make sure you have fuel flow which can be determined if the engine will stay running if you manually hold the iron core in.

It is a process of elimination, good luck.