Another solution is to recover the entire antenna (except for the connector, of course) with the stuff that is sold to 'rubber' coat the handles of pliers and other tools. I suggest dipping it into the liquid at least twice.
I've redone antennas like that before, and as long as you take care to clean the old 'coating' off of the antenna and wipe the thing down with alcohol to get rid of grease and oil, the antenna will look like new again.
I like this idea. These products work very well for this purpose, and are easy and inexpensive to apply. I would certainly give it a try before buying a new antenna. Besides, I'm sure there are a hundred other uses you could find for the stuff.