[http://dfwpcrepairs.com/ipad_repair.html|iPad 2nd Generation had a big flaw in design for the Wifi antenna. For one thing, the antenna on many iPad 2s went bad even without the iPad being repaired or replaced.] We get many customers who call us and ask us to repair them for this issue. I am not sure what causes this problem but after replacing the antenna with a new one, all is fixed.
Another BIG issue is that Apple used to glue the iPad 2 antennas to the bottom of the glass/digitizer from the inside. So if you broke the glass right on top of the antenna, it would damage it and tear into it. They fixed this issue on later models by not gluing the antenna to the glass. So when you took the broken glass off, it would not pull on the antenna and cause it to tear.
Also, if you don't have a lot of experience in fixing iPad 2nd Generations, it is very easy to rip the antenna during repair. The antenna is is screwed to the body of the iPad by 4 screws and it is extremely flimsy. The antenna can easily rip away from the screws and become loose. We have even seen many antennas that go bad after the repair without any physical damage visible to the antenna.
Also keep in mind that some Apple software updates do cause wifi connection issues on certain iPad models.