Soak it in Liquid Wrench or PB Blaster first.
Take a picture. Hopefully some of the stud is still exposed and you can use vice grips. If not, you will need to drill a small hole and use a screw extractor. It will help if you can find a left hand drill bit and drill the hole backwards, that way you are not making more work for yourself. Most industrial supply places have them or order online.
Success! The adapter post twisted off below the surface of the mount. Rather than drill it out and try to tap new threads(didn't want to bring a drill anywhere near my paint), I ordered a new antenna mount and plastic shroud from my dealer. My cost for both was $13.00.
After studying the situation, I decided to use the "two string" method. I attached a string to the end of the cable and another string to the mount. I disconnected the cable behind the kick panel and pushed it through the body after pulling the grommet out. After I unscrewed the nut on the mount, the mount dropped down and I used a grabber with a trigger claw to grab the string. I then pulled the string and the mount up and out between the fender and the hood hinge. As I pulled the mount up and out, the lower string stayed with the cable end. I attached the new cable end to the lower string. After I fished the mount back in between the fender and the hinge, I maneuvered the mount into position. With a little help with a yard stick to move the sound deadening foam out of the way, I was able to pull the cable end into the space in front of the door opening so that I could feed it into the passenger compartment.
As much as I liked the shorter antenna for looks, I have to take the blame for going with a "cheap" product that rusted and caused the problem. No matter what antenna I had, I still had to remove it for the wash. Also, I placed a dab of white grease on the threads to insure easy removal in the future. Sometimes its the little things that cause the problems.
