I'm driving along and the A/C is blasting very cold air as it usually does in this car. Suddenly it just stops being cold. I parked my car when I got to my destination and when I started it up it blew cold air again for the next trip.

The next day I started it up and it was cold, and 10 minutes into the trip it stopped being cold. I got to my destination and when I started driving again later it was cold again.

Any ideas?

Which turns the compressor off for safety reason.

Try hooking up vag-com to the HVAC system and I think it would store a code.

I had similar symptoms on a 99 A8, but turned out to be the fan motor going bad. Here's the thread:

http://forums.audiworld.com/a8/msgs/117012.phtml

Here's the fan replacement procedure courtesy of Audipages:<ul><li><a href="http://www.audipages.com/Tech_Articles/heatac/fanreplace.html">fan replacement procedure</a></li></ul>

If you stop, a few hours later it works again then freezes up again. Typical airflow problem.

this is easily measured by an aircon tech.
Also check the pump is not jamming or loose belt?