Assuming the power to the antenna base (amplifier) is turned ON (there's a way to verify this with VCDS/Vag-Com or even through a menu in the radio itself... do a search), the circuitry inside the base is known to corrode... If you look around, you may be able to find a replacement antenna for not all that much money - although as CCBB said, getting to the underside of the base is a pain on the Sedan models...
Be careful with the Chinese ones on eBay... they're not the same quality, although possibly if you stay in town it should pick up most of the stations.
Yuri