Ultimately, the problem lies in the Wi-Fi Power Save Mode, which turns off wireless whenever the phone goes to sleep. For some of the Galaxy S III units, this seems to negatively effect the Wi-Fi when the phone is awakened. Now, on the Android Samsung Galaxy Tab, you can actually (and easily) set this feature in Settings | Wireless and network | Wi-Fi settings | Wi-Fi sleep policy. On the Galaxy S III, you won't find this setting. In fact, if you go to Settings | Power saving (Figure A), there isn't even a reference to Wi-Fi