Yup. The generator is not recharging the battery while you're driving or it has a bad diode. You can verify that with an inexpensive digital voltmeter. Measure the battery voltage with the engine running and while the problem is occurring. It must be between 13.75 and 14.75 volts. If it is low, around 12.6 volts, suspect the generator.
Tuesday, February 26th, 2013 AT 3:47 AM