WiFi Automatic

This simple app can help you increase the standby time of your device: WiFi Automatic automatically disable your WiFi radio when you don't need it and thereby lowers the battery consumption. It is designed to be used with WiFi-only* tablets - these devices normally don't require a constant internet connection if you're not using them and turning WiFi off can save a lot of battery power.

You can also specify to automatically turn on WiFi again, if you turn on your device. Also, the app can regularly scan for available networks to connect to and re-disable WiFi if no suitable network is found. This way, you are always connected to your WiFi network when using the device.

This app has a similiar effect like setting the "WiFi sleep policy" in Android to "always", except that you can now exactly define the timeout between turning the screen off and actually turning off WiFi.

*if your device has a cell radio, it might switch to 2G/3G which may consume more power then staying on WiFi

You can download the app for free from the Play Store or from F-Droid