Got the Toro out this spring, same type as being discussed, 6.5 hp, self propelled, and after going thru all of the cleaning suggestions of jets, carb, tank and so on and making sure the bulb was priming right, on reassembly and testing, without the air filter installed, same problem, runs the prime dry and stops running. I did an inspection of the filter element that I had cleaned, last fall, and found one of the paper edge was stuck out under the rubber edges. I fixed that, and I can only venture, that some how, the filter works in conjunction with the fuel flow as there is a rubber hose that runs to the crankcase, and that has to pump and suck as the piston action occurs. I took the filter and reshaped the side with the paper under the gasket so that the entire filter seals and bingo, put it all back together, did a 3 pump prime and the engine started first pull, and kept running. Let me just say, I did all of the suggested remedies on the fuel flow issue and this last one did it for me. So which one was the real culprit? Don’t know, don’t care, the lawn mower is running great!