I finally solved my networking issue with my Tivo. I called customer support again and they sent me a list of TCP and UDP ports that I needed to open on my router. Even though I did figure out how to do that from my computer, it made no difference to the Tivo. I thought maybe I needed to redo the Guided Setup (rather than just a plain reboot) but then I got stuck in Guided Setup with no way to exit because it still couldn't connect to my router. I gave up for a little while to watch the Apocalypse show live on my other TV, and was really worried that I'd have to call customer support for a third time. However, while I was trying to reset the Tivo wireless adapter again, I noticed that I didn't put the switch on Client, so I did that. Then I did the manual setup of the adapter using my laptop. It didn't work when I connected to the router, so I connected instead directly to the internet modem and finally success. All I had to do was connect to the Tivo's ethernet port, then it let me finish the Guided Setup at last. What a relief! Next time I guess I'll skip the Guided Setup and just be more careful about resetting the damn wireless adapter.
The Tivo finished updating its program information and now it can get back to recording my season passes again. I don't know why the router is acting up like this, when it's the same one I've had before I lost the connection.