If you go to Settings->Wireless and Networks -> Wifi Settings and then hit the Menu button (the one with for squares on the bottom left) and go to advanced there is an option for Wi-fi Sleep Policy. It looks like the default is to turn off wi-fi and switch to mobile data when the screen turns off? Is this the optimal setting? Wouldn't you want it to never turn off (assuming you are in range of wifi)? That way any alerts etc. are all handled over wifi instead of data?