Just a couple of points to mention here
1) We usually say first with any of these WiFi problems to check the WLAN Power setting. By default it is turned low, but most PDA's I've had won't sustain a connection at that level.
Open Start/Settings/connections/WLAN and hit the Power tab. Make sure the slider is fully Left for Max Performance. Now turn WiFi off/on and see if it makes a difference.
2) The O2 shortcut in Favourites won't connect over WiFi because it is set to use a WAP connection (the old O2 Active APN) starting with wsp:// rather than http:// . WAP will always connect via GPRS because the O2 WAP server is not visible on a normal web connction.