It is normal for a full radiator to vent a certain ammount of fluid as it expands when heated. Without an overflow tank, you will always find the radiator needs fluid when cold. When the system cools after shutdown and the coolant contracts, without an overflow tank with fluid in it (and the overflow hose below the top level of the fluid), the system draws air back in through the overflow hose and the check valve located in the radiator pressure cap.
Before tearing into things, I would first determine how much fluid is being dumped and wether it is capable of being restored to the radiator as it cools. In order to do this, you need to make at least a temporary overflow container. You can buy generic versions of these at Napa or Shucks or you can buy a $.99 clear water bottle at Walmart and ty-wrap it in place. Here is a link to John's jinma site showing how I setup the recovery tank on my 284.
http://johnstractor.homestead.com/AirfilterCoolantRec.html
You want the bottle up near the same height as the top of the radiator with the overflow hose going all the way to the bottom of the tank. The tank also needs an air vent on the top.
If everything is normal, after a few heat/cold cycles, any air will be purged from the coling system and the radiator will remain full every time you check it when cold. As the fluid expands when heated and the system pressure exceeds the rateing on the pressure cap, fluid is pushed into the overflow tank. As the system cools after shutdown and the fluid contracts, the same ammount of fluid is drawn back into the radiator, keeping it full.
If you find the radiator is not staying full even with fluid in the overflow tank, one of 2 things is happening.
1. There is a very small leak in the system somewhere and as the system cools, air is being drawn in through that leak instead of fluid being drawn back from the overflow tank. Since any vented fluid should be going into the tank, any fluid found on the tractor or the ground will indicate a coolant leak.
2. Either a headgasket or cracked structure is allowing combustion air/gas from a cylinder to be forced into the cooling system. These problems usually get worse and as they progress, this excess air pressure can be observed bubbling from the hose in the overflow tank while the engine is running. Higher engine RPM/engine load will = more bubbles. Since the combustion air has diesel fuel in it, you will also start to see an oil residue buildup in the overflow tank. That and to see bubbles is why you want a clear overflow tank.