Mine now, but used to be my dads GX345 with a kawasaki did the same thing when he first got it. Then it started dieing after about 10 min. of mowing and a few later would fire up and mow for another 10-20 min. Took it to the dealer and they replaced the circuit board that has fuses on it located under battery by the dipstick and hasn't had any trouble for the last few years. Its an 02 and that happened in 05 or 06. IIRC the part was under $20 so it might be worth a try.