I too, have been having this problem. Virtually every time I open iPad2, I have to go to Settings, Wi-Fi, and Renew Lease to get the internet connections to work. Sometimes even in the middle of a session, I will have to go back to Settings and Renew.
I am using a 64GB AT&T (but have never activated the cellular function), Version 4.3.5 (8L1). Seems to me the last system update I did is when my problems started.
I have rebooted the iPad and the Router (a Qwest modem/Router combined). I do have a WiFi connection on the Xbox in the same room about 25' from the router. Could this be causing interference? I have not had any problem using a WiFi laptop in that same room.