Until upgrading to Airport Extreme software version 7.2.1 using my Airport Extreme to connect USB disks was working quite well. Now it works not at all. It turns out after spending a couple of hours trying to see what I might be doing wrong that there are many people with this problem. Sadly there are not reports of people being successful in working around it. In my case it was easy enough to swap them back to the iMac which is usually on when I want to connect to the disks. I sure hope Apple gets this fixed soon.
[Edit] -- Changed the incorrect mention of Express to Extreme per the comment.
Until they do there is a way to get back to a working version of the firmware.
- Open AirPort Utility
- Select a base station (to get mine to show up I had to power cycle it because although it was working it would not show up in AirPort Utility
- Hold down the Option key and choose "Check for Updates"
- A complete list of all updates will be shown and you can choose a previous version from the list