Try adjusting the following Advanced WiFi options and see if this resolves the problem for you.
You may have to 'forget' your network in the phone, (tap and hold your WiFi network name in the available WiFi networks list, an options box should appear with the option to 'forget', tap and follow the prompts), then alter the following settings and then reconnect your phone to your network to see if it now works OK.
Not quite sure if the settings are here as I don't know the phone, but go to Settings > Wireless and Networks > WiFi > tap settings (either 3 vertical dots upper right corner or the right hand soft button (key?) below the screen) and tap Advanced.
Find the following options (if available)
1. Keep WiFi on during sleep - select Always
2. WiFi Optimization - disable.
Hopefully this is of some help.