I had exactly the same problem for many months. Tried lots of proposed solutions, but none worked. Airport Express SEEMED connected (green light), and initially appears in the bottom right 'pop up' of iTunes, but when I clicked to connect I got the same error message (-15006), and the AE promptly disappeared. I'm using a VirginMedia Superhub for Internet, and had added the AE just for streaming music.
FINALLY - solved (today):
* noted the MAC address of the AE (using Airport Utility) - this is unique to the AE, so never changes
* went into the Admin settings of the Superhub, and noted the IP address it was allocating to the AE (this was visible BEFORE AE vanished from iTunes - when the AE vanishes from the Superhub too) - it was 192.168.0.13
* THEN manually assigned this IP address to the AE using the Superhub settings
The Superhub restarted, I restarted iTunes, and Lo! all is working fine now for streaming music via the AE.
Not sure how long this solution will last - but I'm pretty sure the problem was caused with IP address allocation, so hopefully all is sorted for a while.
Hope this helps!