06GT4RAD

OK starting batteries are not designed to be completely discharged and then recharged like you are doing. What has most likely happen is when you killed the battery by leaving the Radio on it discharged the battery completely then you recharged it to with the Alt after jump starting and that put to much stress on the battery. Then it died again and you charged it to slow with the low amperage charger. That type of charging is best suited for Deep Cycle batteries. So all this dying and recharging has most likely killed the battery. They simply cannot recover from being completely discharged and then recharged time and time again. Then if the weather has been cold where you live that is the final blow that is killing the battery. I would say a new battery needs to be installed to start with and Ford should cover it under warranty.

Richard