IMac suddenly stopped seeing the WiFi network, which works with every other device in the house

This little script will tell you when you are not connected to the Internet. If you want to Ping (and monitor) your router instead, change the Google.com to your Router address.

It will not solve your no connection problem that can have many other reasons. Like flaky connection to the router, like crowded channel, like a limitation by the IP provider on number of connections, and so on.

To help you solve that we need much more information on your set up and connection numbers.

repeat
    try
        do shell script "ping -c 5 google.com"
    on error
        display dialog "You are not connected to the internet"
    end try
end repeat

As for debugging, hold the alt key and click on your WiFi icon and select the Open Wireless diagnostics (at the bottom). Now you will have access to 2 tools to do some debugging.

I know this thread is old, but I'd like to leave here what solved the problem for me. You need to check if you have the same security in both access points. For example, I had one access point secured with WPA/WPA2 and another with WPA2 only. After changing both to the same, everything was fine.

To check your access points' security, you can do this:

• While holding the option (alt) key, click the WiFi icon in the menu bar
• Click "Open Wireless Diagnostics…"
• Go to "Window" > "Scan" (or press CMD-4)
• Check if the security is the same for both your access points

Solution source: http://forums.macrumors.com/threads/wifi-roaming-issues-two-aps-with-same-ssid.1208584/