Your battery has already been replaced multiple times, so sounds like a problem w/12V charger? Maybe it somewhat works, or is sporadically charging the 12V battery?...
But an easy thing to try is to reset/reboot the media center which controls most of the 12V stuff - its a little pinhole button down on the lower left near the volume knob. Use a paper clip to push and hold it for a few seconds.
I know there can also be a battery drain issue if the key fob is too close to the car while it is parked. Is there any chance there was an extra key fob in/near the car during these issues? Maybe even just if you are keeping the fob on the other side of the wall from the garage? If so, it could be draining the 12V battery every single night, so it finally can't hold much of a charge anymore. Try moving it to somewhere further into the house.
