Apple iPad 2 is having some issues connecting to certain Wifi connections and Apple forum was filled with complains and requesting help. Many claim that Wireless will be drooping N (802.11n) in 2.4 and 5 GHz bands specially if they do not use the mix mode. Apple has officially confirmed that there is a issue and suggested some solutions for that in Apple support.
iPad Wifi Issue Symptoms
* WiFi will only work for a short while, then completely stop.
* Dropping WiFi connection constantly.
* iPad2 shows good signal strength but nothing works via WiFi
* iPad is restarted or wakes from sleep state, it fails to join the known and remembered WiFi wireless network
Suggested Solutions
Fix your Router
* Update Wi-Fi router firmware - All most all the modern routers allows you to upgrade it's firmware. Simply check whether a update available for the router model and log in to your router from a web browser and
upgrade the Browser firmware.
* Use WPA or WPA2 wireless security instead of WEP. Again you should be able to change this setting by login to the router.
Changes for your iPad
* I am not sure how adjust screen brightness will effect the iPad WiFi connection but Apple suggest to switch off the auto brightness and increase the brightness. You can change the settings from Settings > Brightness & Wallpaper.
* Renew IP address of iPad.
Tap Settings > Wi-Fi > Select the Wi-Fi network you are currently using and tap Renew Lease
Apple will be fixing the iPad Wifi problem in the future software updates but until then you can try the above methods.