Android™ lets you set up the standby of your WiFi connection according to how you use it. To check the setup on your device, go to (or) Settings > Wireless and networks > WiFi and tap Menu > advanced.
Then select Keep Wi-Fi on during sleep to set up the sleep mode:
- Always : WiFi turns off as soon as the screen turns off.
- Only when plugged in: WiFi stays on as long as the device is in charge, even if screen is off.
- Never (increase data usage) : WiFi never goes into sleep mode.