Shadowcatche is right. Most converter/chargers (also inverter/chargers) do not charge the engine battery, only the house batteries. You can use a VOM to find out if that's the case.
Our engine battery, which is the original, is almost 7 years old and will go dead in about 3 weeks. I put a Battery Minder on it when we park longer than that.
If your engine battery is going dead in a few days, there is either an unusually large phantom draw or else your engine battery is almost shot. You could pull the engine battery out and take it to an auto parts store or repair shop to have them load test it.
If the engine battery checks out good, then you need a VOM to track down the phantom load.