You've gotten a lot of misleading information. First of all, the generator is incapable of developing more current than it is rated for, and nothing on the car is going to damage it. The radio could be wired incorrectly causing it to run the battery down, but that's a different issue.
Once the engine has been jump-started and is running, the battery is of rather little importance. It's the generator that keeps the battery recharged while you're driving. If the engine stalls due to a run-down battery, it's the generator / charging system you need to look at.
To start the preliminary tests, measure the battery voltage while the engine is running. You must find between 13.75 and 14.75 volts. If that is okay, the important part of the test requires a professional load tester to measure full-load output current and "ripple" voltage. If output current is exactly one third of the generator's rated maximum current, and ripple voltage is high, one of the six internal diodes has failed. 30 amps from the common 90 amp generator is not sufficient to meet the electrical demands under all conditions. The battery will have to make up the difference until it slowly runs down over days or weeks.
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Wednesday, August 12th, 2015 AT 6:21 PM