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.