Kohler CV730S Starts then shuts down

I have a Craftsman GT5000 (Husqvarna built) with a Kohler CV730S 25 HP motor, not sure of the hours as it was a replacement engine. I had to replace one of the head gaskets a month or so ago. Started and ran fine, towed it about 365 miles to summer property and used it about 6 - 8 hours, brought it home, mowed the lawn once. Stopped it to gas up, started and immediately stopped, then would not start, a few hours later same, stated and immediately stopped. I pulled the plugs, both okay, has spark to both, checked fuel pump, pumping strong, changed fuel filter, same result, starts once, and shuts down, then will not start of a few hours. I removed the carb bowl and cleaned it and the carb, both were really clean already put it back together and same, starts right off, the shuts down and no go for hours.

Could be faulty fuel solenoid on carb, or solenoid is not getting battery voltage or due to some other issue is loosing battery power. Also faulty oil pressure switch can also cause the same symptoms.

Appreciate the fast response, that was a thought I had, the solenoid that is, did not think about battery connections. The reason I mentioned the towing 300+ miles back and forth is that I was on some rough back roads and at time trailer wheels were off the ground, anyway was thinking if something became loose, so will check your suggestions out. One look at the carb and I thought is this a rocket engine, tubes and wires, seems over sophisticated to me so am overly careful working on or around it.