I have a murray 13.5 hp rider that I got from an uncle a year ago, the tractor itself is only 4 years old and seems to be in great shape. As of recent I have been having a problem with it dying while running, It stars up right away but does seem to have some idle surge, I engage it and the surge stops and it runs great for about 4 or 5 minutes and then it will start to act like it is not getting any fuel and sputters and eventually dies. On restart it will start right away but just sputter and die again. I have changed the fuel filter going even as far as to buy a see through filter to see if there is allot of dirt in the line but nothing. I not sure where to go with this issue any more.

Run it with fuel cap off. If the vent hole is clogged it will react the way you are saying. Also be sure carb is clean. They will varnish up sitting over the winter.