I was having a similar issue with WiFi loosing it's connection when the screen was turned off. Background data and streaming music would fail to update and the fix seemed to be to turn the wifi radio off and then on again. I found a setting under Settings/wireless & networks/Wi-Fi Settings/ then hit the menu key and select "Advanced" then check the button for "Best Wi-Fi performance". That solved all issues I was having with Wi-Fi connectivity. I'm trying to do some observational testing to see how much this effects the battery life. For me, simply leaving the 3g radio on all day and not turning on the wi-fi will get me from 6am up to about 11pm with moderate use (lots of phone calls, 1 hour of internet surfing, 1 hour of streaming audio and watching an hour long video off the SD card). Today I'm going to try leaving the wi-fi radio on with the settings above to see how things go with battery life.
I also tried changing my router channel, which turned out to be great advice as far as my network performance goes, but it didn't solve my issue on the phone.