Not sure how long you have had the Vette
However it is common practice to put a bypass switch under dash (Or other places) so that you control the antenna up and down. That way it decreases wear on that motor. Maybe someone wired wrong?
In addition, I had my BOSE serviced. I had a cracked board. This type of issue could cause a short.
Just a couple of ideas.
I spent $500 on repairing my BOSE, then removed due to frustration. I still have in a box so if I want factory, I can get it back. However, I love CD's in the car now, clear sound and no suprises everytime I turn on the tunes.