Follow the following as a general guidline: http://support.apple.com/kb/TS1398
Also make sure to renew the lease of the IP. Select your WIFI network when connected to it, by tapping the arrow to the right of it, and from there selecting renew lease.
If the issues continue, try configuring your WIFI network, by following the article here: http://support.apple.com/kb/HT4199
I tried your suggestions, and they did not help at all. Suggesting reconfiguring our wifi, and disrupting all devices in our home is a ridiculous suggestion. It is a bug - plain and simple, so it's time to sell all 3 apple devices.
We have 2 new iPads upgraded to 6.1, and one I iPad first generation still running 5.1.1. Sitting in the same location in my home, at the same moment, the 2 upgraded to 6.1 cannot stay connected or access the line, while I am very happy and stable on the iPad running 5.1.1.
Your reply also mentioned apple knock-off's. All three iPads were purchased at a certified apple store. The stores with the big lines and the great customer service.