Small Engines (Lawn Mowers, etc.): John Deere 345 Tractor, john deere 345, leak down test

Question
When cutting tall grass after a short time the tractor shuts down....just stops, feels like not getting gas...it starts right up but after a few minutes of cutting will die again..again starting right up.....with mower deck off it runs fine......

Answer
Is the deck loading up under neath and choking the engine?  If so raise the height of cut or slow down.  

If it is a deck issue have you inspected the belts on the deck and running to the deck?  

If it is not a deck issue it could be a tired engine.  How many hours are on the engine?  Have you done a compression check or a leak down test?  Are you burning oil?  If so the rings may be shot and the cylinder worn.  Put the front bumper up against something solid, like a wall.  Put the tractor in gear and see if you can spin the wheels.  If the tractor dies I would be looking at the engine if not the deck belts, spindles or clutch.  Hope this helps.