Originally Posted by Sanitylost

You need to change the settings for your WiFi in the phone. The default is that the WiFi will disconnect when the screen goes off.

Do the following from the home screen: Press Menu\Settings\Wireless controls\Wi-Fi settings\Press the Menu Key again\Advanced\Wi-Fi sleep policy.
Once there you can choose between three options.
I have mine set to "never".
There is an app that will place a widget on your screen and you can toggle between "never" and "default". It is called "WiFi Lock"