This problem has been resolved! By following the link in Allen's message, I connected to an Apple advisor who called me in under 30 seconds after I signed up for support. His efforts were thorough but initially unsuccessful … However, he forwarded my case to a senior Apple advisor who accurately troubleshot the issue and made it work. He explained that the airport base station can transmit in either 2.4 Ghz or 5.6 Ghz. By renaming my network in Airport Utility, we were able to force it to use the 2.4 Ghz network which immediately solved the issue. Apparently the base station thought the 5.6 was the better connection but it had some (still unexplained) interference on it which caused the transmission to cut out after a brief connection.
Wow! Couldn't be happier with this ending … thanks Apple!
Tommy