All of the newer Kubota tractors have what they call "Key Stop" this is where either the act of turning the key off or a seat, PTO or pedal switch goes to a state that the Key Stop timer relay becomes activated.
If this circuit looses power there is no way for the relay to energize and activate the solenoid to pull the shutdown lever on the injection pump closed to kill the engine, contrary to popular belief many Kubota tractors do not require a solenoid to be energized to run but it is only energized to shut down.
People need to learn where the shutoff lever on the pump is and learn how to pull it to the closed position. Some engines do have a solenoid with 2 coils, one to hold lever open to run and a larger one to enable the shutdown and sometimes the run coil fails and people get intermittent shut downs causing problems. If the BX has the D902 engine their is a silver or sometimes gray solenoid that you can see energize for 5-10 seconds when you turn the key off. That is where you need to look in case you blow the fuse again and you can pull the lever to the stop position to kill the engine.
On both my Massey MF35 and Kubota L3130 GST they will both run for at least 10 minutes when the fuel valve is turned off, they use up all the fuel in the filters and just about suck them dry until they finally stall out.
David Kb7uns