What year is your mower? My 2004 725G2 did the same thing. It turned out to be the fuel shut off soleniod . On the bottom of your carb, there is a plug with 2 wires. This connects to your soleniod. It could be that you have corrosion at the connection or the solenoid is bad.
If you choked a Smurf, what color would it turn?
I'd give my right hand , if I could be ambidextrous!