Time Machine will NOT work with Airport Disks!
http://www.apple.com/macosx/features/timemachine.html
It also specifically says: "You can designate just about any HFS+ formatted FireWire or USB drive connected to a Mac as a Time Machine backup drive. Time Machine can also back up to another Mac running Leopard with Personal File Sharing, Leopard Server, or Xsan storage devices."
Surely, they would have included the Airport Extreme Base Station in this list if it was supported.
I really hope there will be another firmware update for the AEBS which will bring compatibility with Time Machine, because Time Machine was the only reason for me to buy an AEBS. (I only use it as a small backup server, I don't even have wireless networking enabled. There were other solutions, e.g. from Synology, which are faster and more reliable than AEBS disk sharing, but Synology stated their network drives would not be compatible with Time Machine.)
Mac OS X (10.4.10)