David,
A couple of things here. One, in normal starting operations in cold weather, does your Pre-heat system for the glow plugs work as it should? That is, when you push on the start button in cold weather, doe you get a delay before it actually cranks? If so, that would tell me the glow plug heating system and, the engine ECM (if that little Kubota has one like the later models do)is working as it should.
Second, all diesels, big, small, intermediate, have some sort of "fuel shutoff" to shut them down because there's obviously no spark system to shut down like gas engines. Some are mechanical shut offs from cables, levers etc. but, about 98% of them now days use an electrical solenoid to shut the fuel off.
Is it possible that, that shut off solenoid is stuck in the "shut down" position? I don't know how close in operation your model is to the later 7.5QD models but, I would assume that as far as the diesel engine side, it should be darn close. A diesel engine is a diesel engine, period. Just how the A/C voltage is regulated and controlled in the earlier models as opposed to the later ones, may have some differences.
I'm not a fan of starting fluid in diesel engines but, since this is a "not so high tech" diesel", it might be worth a try but, only sparingly. I'm assuming that your model does not "throw" any codes, like the 7.5QD and larger versions do but, that's just an assumption.
So, as has been suggested, I'd make sure of at least a half tank of diesel, no clogs in any of the fuel lines, the fuel pump on the little Kubota is working, the Glow plug system is working, there's plenty of oil in it, and of course, if you find any sort of "shut down solenoid" or, whatever means that little Kubota is shut down by, that it's working properly. Just some ideas here. Let us all know what you find out.
Scott