There is a toothed whip that is part of the antenna mast. The teeth on this whip is what tends to break up after a lot of use. Wear on those teeth is accelerated when the mast is bent.
The fix is to replace the mast which includes the toothed whip. Sometimes it is necessary to disassemble the scroll part of the mechanism to remove the broken pieces of the whip. The instructions that come with the new mast usually describe how to change the mast.
Other gears that commonly break in the power antenna? There aren't any others that commonly break.