The next day, the same symptom occurred -- my application was not communicating with the internet. I try connecting to it via its AP mode, but since it restarts every 8 seconds due to Watchdog, that doesn't work so well. So I load up a simple app on the board with just setup (to disable watchdog) and no loop, and then I can connect to the built-in AP and bring up the web interface. The main page comes up fine, but when I click on the "page" names on the left side menu, the browser just spins its wheels. I could not make any changes. It appeared that the client mode was still set to connect to the correct wifi network, but there was no IP address. Perhaps the password was corrupted this time? I even tried the factoryRestore sketch, which as far as I could tell did nothing this time (I've had it work in the past).
So, I plugged in my older DigiX board, ran the same simple sketch, was able to access the settings just fine and get it re-connected to wifi as a client. The older board (my original Kickstarter purchased one) is running OK for the time being, but I suspect something is not right here.