The A6 uses multiple radio antennas. The diversity box is under the
rear parcel shelf. All of the antennas come to this central point. The
AM antenna is in the windshield and the FM antenna is in the rear
defogger grid near the bottom. Diagnosis of this problem could get
expensive and I recommend taking it to a Audi dealer.

If you do decide to go to Audi I would see if you had the ability to
try another radio from another Audi to make sure it is not the radio