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There isn't any tie between the engine batteries and the generator in MOST cases. The only way they would is if they engine battery was used to start the genset. I would start by checking them to be sure they don't have one with a short. They don't ordinarily get any charging when the genset is running...........so IF you have a short someplace in the chassis wiring that would drain them. Have them load tested to be sure. And if there was any changes in the wiring or the batteries were taken out recently, let me know. All follow ups are included in our fee. R.J.