That is the same thing that happened to me today with a Sears riding mower, not a tractor. It is about 10 years old and has worked well but today it started to sputter and back fire and then died. It would start, go a little and die again. I hope you get an answer from someone who knows what they are doing because it will probably solve my problem as well

1) chk/clean gas cap vent with a small stiff wire.
2) pull engine shroud sheet metal - clean fins well.
3) if engine still shuts down, immediately chk for good spark at plug. Coil may be going bad when hot.
4) if no help, post back with latest details.

That's it - spark plug, at least in my case, and it may be all that is wrong with the original poster's machine. I cleaned the gas cap vent but it keep shutting down. I took out the plug and it was fouled. Replaced it and all is well. We by-pass the simple things and always think it is more complicated than it really is. Thanks rcbe for the tips.