I have a 2007 BX2350 with the same problem. I have replaced bot Fuel Filters, ran clean fresh Diesel and it ran fine while mowing until about 45 minutes or so then it will start Pulsating when running, with Throttle at 3/4 (towards full power) it is surging and sputtering loosing power. Turning off the Mower deck helps for a short period but then starts up again and will actually quit running unless it is throttled down. If you turn it off and let it sit for 10 minutes and restart it, it will run fine for about 30 minutes and do it again. I actually ran the fuel down to below 1/4 tank and when this happens the fuel level will bottom out or jump.
This was occurring even before replacing the fuel filters and lines.
Thinking possibly the Fuel Pump.
Any other ideas???