This might be a stretch but I'll throw it out anyway. I bought a Kenwood
radio/cassette player a few years ago and wired it so it would stay on
without the ignition switch just like the original. It turns out that even
when the radio was turned off it still drew a couple of amps...enough to
kill the battery if it sat for more than a day. What a stupid design.
Have you checked to see if there is any current draw on the battery when
the vehicle is shut off? Most chain parts stores can check this for you
quick and easy in there parking lot.
Good luck.

Tom Brobst