I had exactly the same problem, the battery went dead even with the
faceplate off and only after I installed a high end stereo. I discovered
that the amp was warm to touch after extended hours with the unit turned
off. It is easy to solve though, run the main power to the stereo from
something that is activated only when the key is in place like the key
warning buzzer. If you have a really high power stereo you need to take the
power from elsewhere but use that key alarm circuit to trigger a relay.
This way you can listen to the radio just by inserting the key and your
battery won't go dead. You will also need to connect a line to your stereo
that is always on so that the clock and memory will remain intact, you can
use the existing unswitched circuit that you were using before for the
main power. The drain on this is so low that it won't bother anything for
long periods of time. If you store over winter perhaps you could pull that
fuse or keep the battery charged.
 My guess is that the manufacturers of these stereos are using cheap
switches and just turning off the indicator lights thinking that you will
be using a switched circuit in the car anyway. Certainly wrong for older
VW's anyway.

Tony

85GL Westfailure