It's Window's Fault - I Knew It
The weird thing about my issue was that it wasn't a real problem. On the computer that was disconnected all you had to do was Disable it and then Enable it and it worked like a champ. No settings needed changing, no tweaks were required- nothing. All that needed to happen was for the wireless network to be tried again. Was was really weird was that Windows thought the network was working just fine. It said Connected, the icon in the system tray never changed to have the red X on it, nothing. As far as it was concerned, the network was up and running.
Windows, till the end, I grapple with thee.
The main difficulty in troubleshooting computers is that people always think they have all the information when they usually don't. I can't count the number of times I got phone calls from users who just "suddenly" started having trouble with their computers when they hadn't done "anything." After hours, I'd find out that they had unplugged the network cable over the weekend to plug in their laptop. "Oh, I didn't think that would matter." And, I was high-end computer systems administration, I didn't even deal with the real knucklehead stuff.
And, so it was with me. I didn't "suddenly" start having trouble with my wireless network. I started having trouble with my wireless network when I started working from home on the same days my wife was working from home. More specifically, I started having trouble when one of our laptops was turned on when another was already on. I wouldn't connect the dots for weeks, until one day while sitting on the couch with my laptop, my beautiful wife joined me and turned on her laptop, and my laptop promptly lost its network connection. Ah-hah!