Even though this post is older, I will try to answer this for future users also. lol
I know this problem b/c it normally isn't a problem. lol In your case it is b/c it's just sucking the battery down. When some people hook up the wires from your stereo to the truck, (just talking about a normal radio install here) you can hook the radio/clock/screen or etc. to the battery directly, or you can hook it up to a 12V like most do. Now in your case it is hooked up directly. Just need to pull the stereo and hook the stereo back up correctly and check your wires out to connect it to a 12V.
If that isn't it, then idk whats wrong. But it seems that it would just be hooked up directly to the battery.
When I was in high school we used to hook the stereos up directly b/c we sat in our cars in the parking lot and didn't want to turn the key to use the stereo in our vehicles. Hope this helps anyone.