There is a huge amount of misinformation in this thread. You don't have anything wrong with your iPad and neither is there anything "wrong" with the router.
The wifi problem being experienced by iPad running iOS6 results from Apple having implemented a protocol known as WMM. Quite a few routers do not routinely support WMM and some are not able to do so at all. As a result there will be some networks you will have trouble connecting to. If it is a network you need to connect to, like at the office, ask the network administrator if he can enable WMM.
Otherwise, if you experience a problem, go to network settings and click on "Forget this Network" then go back and rejoin it. It is only a temporary fix but it will get you online for a while.