Recently, my AirPort network hit a major snag. While my main Base Station continued to function properly, AirPort Utility (on my Mac and iPad) indicated that my three subsidiary AirPort devices had dropped off the network (see image above). Selecting any of the devices in the bottom row resulted in a "Device not found" error. Confirming that these AirPort devices were indeed MIA, none of my wireless devices (iPhone, iPad, MacBook Pro) would connect to them. The situation with AirPort Utility on my iPhone was even more disturbing: no AirPort devices showed up at all!
For my iPhone, Apple's recommendation to power down the device was what was needed to get its AirPort Utility back on track. After a restart, all my devices were again listed on the phone.
If you are experiencing AirPort problems similar to what I've described here, take heart. Your hardware almost certainly does not need any repair or replacement. Based on what I've read online and my own experience, at least one of the suggested fixes should remedy your situation.