Thanks Slugfest. The symptom appeared for me when I changed my router's encryption from WEP to WPA2. I followed your instructions, and once I figured out that "Click the - (delete) button" meant clicking on the "-" (minus) button, everything else went smoothly and my MacBook Air now reconnects automatically. Thanks for the "step by step" instructions!
This worked for meexcept I had to restart after #8 and after #10 reorder Preferred Network list.
9. Turn it back on.
10. Select and login to your wireless network. This will re-save your connection underPreferred Networks.
10A. Move my wifi network to top of Preferred Network list
11. Close your laptop and reopen it to test whether it worked.