So the batt holds around 12 to 13 volts,the alt puts out let say 14.5. Car runs for a a long period of time.If the alt is not working it is not putting 14 some odd volts back in. If it is running on the batt the car will in fact stop running sooner or latter. That statement comes with a warranty! This car and I'll venture to say that your car had a bad connection someplace.You just happen to find it. i would suggest using a volt meter to check the stating current at the batt, starter and then the alt.