Welcome to the land of being a mechanic on a sailboat. I once owned hull #27 and had plenty of chance to familiarize myself with the mysteries of the engine. For me, first I'd want to know if the engine was overheating during all of this (think engine water pump or raw water pump). I'd hope nothing seized up. You could have everything from a loose belt, or very worn belt to more complicated. I'd take a look at belt tension first, then remove the belt and see if the alternator turns easily (it should). Alternators rarely freeze up in my amateur experience. Ruling that out, I'd try spinning the engine (fresh water) pump. You should be able to turn it. On a recent voyage, on a friend's elderly boat the shaft to the fresh water pump literally broke off. It became a simple matter to replace the pump. While you are at it, since you already have the belt off, check the raw water pump...make sure it looks good, not leaking, impeller good etc. I'm pretty sure you will find the answer just looking carefully. I take it there were no other symptoms. 

You'll have to take the belt off to further diagnose the problem. If you do find it's the engine's water pump, (not the raw water pump) you may want to chat with these folks for a replacement. https://www.kumarbrosusa.com/kubota/water-pump-v1200.html  That site will take you to a company - Kumar Bros. - that stocks water pumps for Kubota engines at a reasonable price. You'll have to select the correct pump for your engine. If you find it's the alternator there are many local shops that will be able to rebuild you alternator for you. Good luck.
Bill