if memory serves me right, when a diesel engine starts running, it will continue running as long as it has fuel and air. kahit ilublob mo pa sa tubig. kahit kaluluwa na lang yung baterya. so it think you can drive it to your talyer for a look-see.

alternator's fault? puede. but it can easily be checked at a good battery shop.

and yes, batteries die abruptly. usually when you are in a hurry the next morning. heh heh.