I have seen similar problems on the iPad 3, the carrier network or wlan show good signal strength, however the iPad is unable to breakout onto the internet. However after switching the wireless radio off and back on this seems to resolve the issue, I have also tried a power-cycle of the iPad. Just in case there is some type of build up, but the problems re-occurs.
Thanks for helping. I tried your first suggestion and also turned the wireless modem off then back on. The two in combination seemed to fix it.
As an aside I find the iPad2 needs a stronger wireless signal than other devices eg my laptop will pick up a weak or medium signal - but the iPad needs a really good signal to connect.