Same issue, albeit with an older Airport Extreme, which suggests at least that buying a newer version of the hardware isn't the obvious solution. The Airport Utility (v6.3.4) isn't providing solutions either. I've tried setting permissions on the Airport to access via Account as well as Device password to no avail.

MacBook Pro, late 2012

OS Yosemite release

Airport Extreme circa 2005

I can still access the airport extreme from an iOS device using airport utility on there so it's a Yosemite bug.

I am having the same issue also,  after Yosemite update I can't reliably connect to the external drive connected to my 5th gen AE

I just noticed after removing the extreme router in the airport utility it went to search for it, internet still worked.

A bit, maybe an hour, later on I checked and it had found it again, showing a green dot. This maybe why people are having intermittent problems.

try to shut down the firewall and set up your extreme en then turn the firewall on.

it works for me

I'm having the same issues as stated above. Interestingly enough, I am connected wirelessly through my airport extreme and can access the internet. But I cannot connect to the device to setup time machine and the device does not show up in the airport utility. My firewall is turned off and I still cannot connect.

That fixed disk access?

Same issue.  Disks attached to Airport Extreme are not available.  Finder can't access.  Airport Utility sees Internet but not Airport Extreme base station or Airport Express extension.  I noted the firewall suggestion above.  No effect.

I know this is going to sound lame, but i was having this same problem earlier and simply restarted my computer and guess what...it fix it. Got time machine connected and airport extreme showing up in the airport utility. If you haven't already, I would give that a shot.

I went to Airport Utility and disabled file sharing, updated Airport Extreme then went back re-enabled it.  After the Extreme restarted, it seemed to be working.

I am having a similar issue.  I upgraded to Yosemite and lost access to my printer which is connected to my Airport.  I initially thought it was a problem with the printer but after connecting the printer directly to my MacBook Pro, it works.  However, I still cannot print when it was connected to my Airport. 

I opened up my iMac which has not been upgraded to Yosemite and it can print wirelessly via the Airport.  So I know my Airport is working which I also know from my MacBook Pro because it has not lost access to the internet.

I opened up my Airport Utility and can see that i am connected to the internet but cannot pull up the airport itself to allow me to reconnect to my printer (just as others cannot connect to external hard drives). 

I suspect its a bug with Yosemite and am hoping a fix comes soon.  I will let the airport utility cycle overnight to see if it finds my Airport similar to others who merely waited.  I am on 28 minutes and counting for it trying to find the Airport.

Update.  Airport access for attached devices has returned to normal.  This was after a reboot.  However, I had previously rebooted and had no access to Airport disks and no Airport Utility access to either base or extender.  Will access remain?  To be seen.

Hi Guys, I had the same problem and found this article that references Lion, however, after following the instructions my 27 iMac running Yosemite I am able to access my two Airport Extremes.  Hope this helps.  Click following link for the instructions:

AirPort base station not seen or "An unexpected error occurred" appears in AirPort Utility 6.3

Thanks owl mamma but it did not work for me and nor did my overnight wait for the system to find my airport.