I had this problem on my integra. The problem as mentioned before is that the antenna is not extending fully, so when it retracts, the motor thinks there's more antenna to retract and keeps on turning. The click is causing by the motor gear teeth slipping off the plastic gear teeth on the antenna mast. The way I solved this is to help the antenna extend fully by lightly pulling it upward when it extends to the top, you'll notice the motor is still turning even though the antenna stopped moving up. Then the antenna will be fully extended and when it retracts the motor turn off when its fully retracted.
Remember, I did this to my 1990 Integra and it seemed to work for a while, but it needed this treatment every few months. So there was something else wrong somewhere. I dont know if I'd try this on my NSX.