What's the Sears 917.xxxxxx number?
A couple different things could be the culprit- Fuel & spark.
IF the gas cap isn't venting properly, the tank could be pulling a vacuum to the point that fuel flow is inadequate. Loosen the cap for a few seconds to test.

A restricted fuel filter could do the same. IF that's the case, it would probably run indefinitely if no load was on the engine, but occur more quickly, the harder the engine was working.
A fuller fuel tank wold probably also make this problem occur sooner than a nearly empty tank. (amount of air space to "depressurize")
Also look for a cracked vacuum line to the fuel pump.

Check the spark immediately after it quits. You might check it with a cold engine first, so you have something to compare it to.

I have a dlt3000 that will not start unless I spray startimg fluid or gas into the carb then it runs until the gas rins out if I try to restart it it back fires through the carb with a flame of fire. Any ideas is out of time if so can anybody tell me how to time it. It has a Honda 17.5 h.p engine. Please help me

For what it's worth, some carburetor fuel/air systems have a thermostatic choke adjuster so that the air/fuel mixture can change as the engine goes from cold start to normal operating temperature. I had a car that exhibited the exact same behavior. If your mower starts when cold but as it warms up begins to act as if it is stuck at full choke than this is it. If you follow the choke adjustment from the carburetor you should come to a disc-like can the contains the length of bi-metallic element coiled up within it. It could have worked loose or worse require replacing. It's simple to do either.