I also had a similar prolem on both my 1st gen and New iPad after upgrading to iOS 5.1.1 via WiFi connection. It will connect for a while but the all of sudden not be able to access the Internet, even though it's connected to my WiFi modem.
- Never had issue prior to upgrade
- Issue only appeared several hours after upgrade, but was then consistent with loosing Internet every 2-5 min
- iPad shows as connected to the WiFi, but is just looses Internet connection
- Upgrade done "over the air" via WFi
- No other device (computer, iPhone, XBOX & etc) using the WiFi has any issues
- Tried to reset WiFi modem with no improvement
- Tried to restart iPad's with no improvement
- Connected to 2 other different WiFi networks with no improvement
I found that by turning off WiFi from the Settings -> General -> Network -> Wi-Fi -> Wi-Fi (On / Off) slide button and thn turning it back On fixed the problem for a short while and made it able to reconnect to the Internet. Now after having done that about 10 times the problem seems to have disappeared for good.
So maybe the iPad Wi-Fi controller needed a bit of a "massage" in order to work properly with iOS 5.1.1
Let me know if this works for y'all