Probably broken plastic wire inside that makes it go up and down. Had the same problem and took apart and ordered new mast.
== == How do I get instructions on replacing a power antenna on a 2004 corvette convertible?
Remove left rear wheel plastic housing cover under the body you can then access the antenna motor.
Replace the power antenna assembly.
Remove the wiring harness from the bottom of your 1987 Chevy Corvette power antenna. Remove the power antenna retaining nuts. Reverse the process to install your new power antenna.
== ==
95 % of the time the nylon cord that moves the antenna up and down gets stripped. The power antenna motor is going to cost about $200.00. The antenna mast is about $40.00 which comes as part of the nylon cord. The motor that drives the antenna must bestill working. The procedure to fix takes about 15 minutes. Remove the nut that secures the antenna and slowly pull the antenna out od the socket. Take the new antenna with the nylon leadand feed it into the socket hole. You can then secure the antenna in place with the holding nut.
There is a plug on the front of the fuse panel that you can disconnect. It should be labeled and I believe it's an orange wire.
The antenna relay could be bad
unplug the electrical from the antenna. replace antenna.
Yes there is a fuse. Determining which fuse protects the antenna motor may require some detective work. It may be the radio fuse, or it may be a separate fuse, perhaps shared with the rear-window defroster grid.
Below the blower motor
I have the same problem on my Nissan Altima, it is the antenna motor. Replace it.