After a little investigation, I found that the JD fuel system on your tractor uses a fuel filter and head assembly manufactured by Stanadyne. Their product terms it as the 'Fuel Manager'. What you are experiencing is the fuel filter is draining back into the fuel tank leaving vapor in the fuel filter. When you start the engine, the vapor causes rough running, likely some white smoke and shortly after, the engine quits due to air in the injection pump. This filter system has an air bleed valve on the head plus it has a water drain valve on the bottom of the filter element. Both must have a solid seal or air will be pulled into the filter while the engine is running or allow fuel to back drain into the tank. Your symptoms state that after being shut down for several days you have these problems. Somewhere in your fuel supply John Deere may have installed check valve to prevent fuel from back draining the filter into the fuel tank. It may be much worse when you tank fuel level is low. Stanadyne suggests that if you have starting issues to use the hand priming pump to refill the filter before you attempt to start the engine. If you do that before you start the engine, there should not be any air ingested into the injection pump. Once air gets into the pump and the engine shuts down, you can use the priming pump to assist in purging air from the pump and injection lines. Find a diesel injection shop that provides parts and service for Stanadyne fuel injection. Most shops can do this.