Gramarye, the hints in your post helped me solve this issue that has been nagging me for over a year! Here are the steps I took to resolve:
1. Click the finder icon in your dock
2. Press command-, (comma) or click on the word "Finder" in the menu bar and click preferences
3. Click on the General tab
4. Make sure there is a check mark in the box next to "Connected servers"
5. Verify that your airport disk now appears on your desktop. If not, connect to it manually the way you normally do.
6. Click on the Apple logo in the menu bar
7. Click on "System Preferences"
8. Click on "Accounts"
9. Click on your account
10. Click on "Login Item", to the right
11. Look at the lock in the bottom left of the window—if it is locked, click it and enter your credentials to unlock.
12. Drag your airport disk from the desktop into the space where login items appear (you may already have stuff there, which is okay)
13. Put a check mark into hide box next to your airport disk
14. Close System Preferences
15. Restart your computer
16. Once it is done rebooting, you will see your airport disk appear on your desktop
17. Start a program that needs to access files on your airport disk (e.g. iTunes, EyeTV, Plex, etc.)
18. The program in step 17 will start without giving you an error that it cannot find the needed file
19. Jump around giddily and/or laugh maniacally
Gramarye, know that I could not have figured this out without your tips, so THANK YOU!