It's hard to see how a running engine could cause problems. Are you sure that's actually what caused the problem? seems from yhat you have said that there is no reason to link the running engine with the charger going bad, correlation does not imply causation
. Chargers sometimes fail for a variety of reasons.
If you are charging from your car battery until you get battery low voltage then your gonna kill your car battery pretty quick. Normal car batteries aren't designed to be discharged more than about 20% of their capacity on a regular basis, they are just designed for short sharp bursts of power to start your engine not for sustained deep discharging. You really need a special deep discharge battery for what you are going.