Maybe a last resort…
Go to the folder /Library/Preferences/SystemConfiguration
Delete the files:
I would try it, but …WARNING: this will kill every network setting and preference! Copy the files to a secure location before you do this! WARNING! Danger, Will Robinson! - YouTube
Did I say…WARNING? 
just a thought - what about any firewall protection you may have on your Mac like little snitch or scudo etc. ?
No firewall running on the MacBook Air (I’m behind enough firewalls already I hope). I tried deleting the preference files and even anything that looked remotely like a wireless preference file. No luck, unfortunately.
I’m going to blame this problem on sunspot activity (even though we’re not at peak activity right now). There’s no other logical reason that avoids getting into 1s and 0s.
Thanks again, everyone! You’re all a great tribe to be a part of.
When deleting files that might be difficult to reconstruct, I Zip them, then delete the originals. This gives the user a way to restore the previous conditions and settings.