It sounds very much like a classic case of the vent hole in the fuel tank filler cap being plugged up preventing fuel from leaving the tank due to the vacuum that forms inside the tank when the hole is clogged.
Try loosening the cap to see if that keeps the event from happening, or you can just go ahead and clean out the vent holes with a stiff wire.
If that does not solve the problem you need to confirm that the engine is still making a spark at the spark plug when the engine dies.

Thats typical of the new model Obama lawn mowers! They have designed them to run great for 15 minutes, then they go all flabbergastingly inferior to an old 15 year mower, and you are dead in the water.
how do i know this?
I was given one that runs just like yours! I have replaced just about everything on it, but it must have a hidden item that causes it to run for a while, then gives it up, and snorts, coughs, squirts clouds of smoke, thumbs its nose at me---and quits! I have changed every changeable thing on it, to no avail! It is now reclining in the back yard, hoping I'll relent, and allow it back into the fold! Will I?? Next trip is to the place where they crush everything dear to the hearts of man-the scrap yard! By: Rusty jones

Since that mower is probably at least 15 years old, you can't blame it on Obama.
Some people (not you) refuse to check the things offered on this forum, try posting the same thing on another forum, don't like that answer either, and then put the blame elsewhere.

Mownie however, offered very good initial advice.

I would add that you might want to check the fuel filter. It might be on the ragged edge of too clogged.

Bill, if you are sending me that helpful info--the mower i have is one made early this year! The owner traded it in, to me, for one made about 6-8 years ago. Even a mower repair shop couldn't fix it-they told the owner to take it home and set it on the curb, and somebody would give it a good home.