Hello & WELCOME to LMF...
Love the big industrial mowers... & Kubota builds the best small diesel engines for the job...
The Hustler 4400 is a Very well built tractor... What mower deck(s) do you have for it? Did you get a snow blower? & do you have the full cab... You can do a Lot with that machine ...
To your problem, have you noticed when the engine dies, is the fuel shut off solenoid releasing and stopping fuel flow to the rack?
Check that solenoid and its associated wiring.... :smile:KennyV