• A device shows full Wi-Fi signal strength, as it normally does at home.
• Almost daily, the device stops being able to connect to the internet over Wi-Fi, but doesn’t report this as a connectivity problem — connections just sit there, spinning, waiting, until they eventually time out and fail. (Like AT&T in Manhattan.)
  This happened most often on my iPhone 5 with the latest iOS version (6.1.4), but it also happened with the previous version (6.1.3) at the same frequency.
• Connectivity could be restored instantly, every time, by turning off the Wi-Fi, turning it on again, and letting it reconnect to the base station.

Great troubleshooting by Marco Arment. If you have WiFi connectivity problems between an iOS device (iPhone or iPad) and use AirPort Extreme, go check the solution on his blog.

(Via marco.org.)