I have a craftsman TY4000. Been having this issue for the past few months. I can start it right up and let it idol as long as I want. But when I actually ride the thing it dies after about 30 seconds a minute. After it dies I can't get it started again (unless it sits for a good while). When I try and turn it over, the motor spins a couple times and stops.
It sounds like it's running out of fuel at high load, maybe the float in the carb needs adjusting. It could also be sticking slightly, only allowing a small amount of fuel into the carb, just enough to idle but not enough to maintain a higher load on the engine.
It could also be a dirty carb and once you start moving the mower it dislodges some crap that blocks the fuel flow somewhere and makes it stall, then falls back down after its sat for a while.
Also, if I read your post right, it will only turn over a few times after it stalls? If so, could it be getting too hot and seizing up?
I have this experience with my LT2000 and it comes down to ethanol fuel absorbing moisture, and when enough water passes into the fuel filter it locks the passage of fuel to the carbeurator. I pinch the fuel line up stream from the filter, then disconnect the filter and shake out any fuel and water, then spray ablast of carb cleaner in the filter to back wash. Reconnect the filter and remove the pinch and i am good to go for a few months. I have also found that if I use an Ethanol additive to the fuel, this does not happen with any great frequency. The additive (Lucas, Stabil ,or Staron) absorbs moisture, so it is good for the whole combustion system, and it enhances the hold over storage of fuel.
