What you should see..
It's the regulator/brush assembly. Read on.
With the car running, the voltage should be between 13.8 and 14.4 (not sure about the high number), unless you have "everything" on and the car is idling.
If you're getting 12 volts with the car running something is wrong. It's possible that it's a major electrical load, but that's easy enough to determine: lights, fan, rear defroster, seat heaters.
That out of the way, probably the alternator is "weak", the most likely cause being worn brushes. On some Bosch alternators, the regulator and brushes are a single assembly, and easy to change. I'm wasn't sure if VW used these, even about my car (an '00) but according to the Russian parts site
http://www.vagcat.com/epc/cat/vw/GOLF/2000/203/57/2461102/ the car definitely has one.
These alternators will start to fail by running as you described, i.e., by intermittantly not charging. This indicates the brushes are worn out.
The voltage regulator is available at any of the usual outlets, as well as NAPA. Unplug the alternator at the connector. According to Bentley, the A4 has a protective cover. Remove the 2 or 3 screws to remove the cover. Then remove the two screws that hold the voltage regulator on (look at the new one). Remove the old regulator/brush assembly. You may have to rotate it to get the brushes to clear, but Bentley doesn't mention this so it may not be necessary on current model alternators.
Install the new one. Most have a slot which accepts a thin plastic tube, such as a WD-40 tube, for the purpose of holding the brushes retracted until the assembly is installed.
I've been through several of these on my MBZ since '81. They're easy to change out.
NOTE: Somewhere around '02 or '03, the replacable brush/regulator assembly was discontinued. Apparently these are identified by no protective cover. And a $200 pricetag on a replacement alternator.
- stan
'00 Golf (Rocketchip II, 520, TT 17 wheels, Valeo E-codes, and probably a Bosch alternator.)