How could a solar panel drain my battery?
As pjc50 mentioned in his comment, most solar panels have a blocking diode in series with one of the output leads. 

In the solar panels that I have, this diode is located in the junction box on the back side of the panel. 

The diode needs to be able to handle the full current rating of the panel. 

Most likely cause of the problem that you are seeing is that this diode is shorted.