Why won't Airport Utility recognize my functioning Airport Extreme?

On your Mac.....

Click on Settings (gear icon on the dock)

Click on Privacy and Security

Click the Firewall tab

If the Firewall is "On", then click to turn it "Off"

Click Apply if asked and close the windows

Restart the Mac and also restart the AirPort Extreme

Check to see if AirPort Utility can find the AirPort Extreme

If yes, you can open AirPort Utility and navigate to check on the passwords. Once you have done that, you can leave the Firewall off if you want, or turn it back on......which may make the AirPort Extreme disappear again in AirPort Utility.

Another option.....if you have an iPhone or iPad handy....and you have AirPort Utility installed on the iOS device, check to see if the iPhone or iPad can "see" the AirPort Extreme in AirPort Utility.

If it can, tap on the AirPort Extreme

Tap Edit

Tap Advanced

Scroll down and tap on Show Passwords

If you do have an iPhone or iPad, but do not have AirPort Utility installed on the device, go to the home screen and tap on App Store. Then tap on Search and type in AirPort Utility to get the process started to download and install the application on your iPhone or iPad.

If all else fails, you will have to reset the AirPort Extreme using a Hard Reset to restore the original default settings to the AirPort Extreme. To do that, with the AirPort Extreme powered on, hold in the reset button on the back of the AirPort for 7-8 seconds and release. Allow a full minute for the AirPort to restart back to a slow, blinking amber light.....which indicates that the AirPort has been reset and can now be set up again.

There is no guarantee that a Hard Reset and reconfiguration will help, but we are out of other options at this point.

If the AirPort Extreme still remains invisible after the Hard Reset, I suggest that you take the AirPort Extreme to an Apple Store.....if you have one near you.....or contact Apple Support directly for advice. The link is just below.

Contact Apple for support and service - Apple Support

Have you power cycled your network as a basic troubleshooting step? If not, now might be a good time to do this.

Power off the entire network....all devices.....modem, AirPort router, computers, printers, etc.....in any order that you want

Wait a full minute

Start up the modem and let it run for a few minutes

Start up the next device connected to the modem and let it run a full minute

Keep starting devices one at a time until the entire network is back up

Check the network to see if AirPort Utility can "see" the AirPort Extreme.

Would it help or be advisable to reset the Airport Extreme, and if so, how?

The AirPort Extreme is not the problem. The problem is Yosemite, which tends to "lose" AirPorts on a fairly regular basis.

So, the next troubleshooting step would be to check some settings on your Mac.

To do that, open System Preferences (gear icon on the dock)

Open Network

Click on WiFi on left panel to highlight it, then click Advanced at the lower right

Click the TCP/IP tab

Make sure that the setting for Configure IPv6 is set to Link Local Only

Click OK, then click Apply in the next window.

Then, repeat the entire process as above except click on Ethernet to highlight it and proceed.

Restart the Mac and restart the AirPort Extreme and report on your results.

Nice work, glad that this solved your AirPort Extreme issue.

The camera recognizes the Extreme base station and correct user name but won't accept any known password, including the one that has always worked

The most common cause of connection difficulties like this is that Apple unfortunately uses non-standard naming protocols for wireless network names and device names.

The Canon device is likely expecting the wireless network name and password to follow standard protocols. That would mean that the wireless network name that the AirPort Extreme is producing should be......

Short....8-20 characters, using only normal letters and numbers

No special characters in the name like an apostrophe, asterisk, dollar sign, etc

No blank spaces in the name

So, if your current wireless network looks anything like this:

James Wittmer's Apple Wireless Network

The Canon camera might "see" the network, but it will likely never connect.

Try a wireless network name like:

JWWireless

Use the same rules for the wireless password. 8-12 characters is best.

Sorry, typo. On the first step above......Click on Settings.....that should read click on System Preferences (gear icon on the dock).