I'm using a Wifi shield (Arduino Wi-Fi Shield - DEV-11287 - SparkFun Electronics) on a weather station. I've noticed a problem.
As part of a test, I unplugged the power from the wireless router it was talking to. As expected, the Arduino application noticed a dropped TCP connection and started trying to reconnect. When that failed enough times, it used the watchdog timer to reboot the Arduino, on the grounds that it needed to reset everything to get a connection going again.
That worked fine, but after the reset, the Arduino diagnosed a missing Wifi shield. I'm guessing the watchdog reset did something bad to the shield, and it stopped responding.
The fix was to hike out and power cycle everything. That's not a great solution for a weather station in the middle of winter; people looking for a very high reliability, recover-from-anything wifi solution may need to consider other options.