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You need a computer to set it up first. For Apple routers, you need to run Airport utility app.
 
First turn the ipad off and on again. I had a few times with my ipad when I had to do that to get it to see a network.

Things to check:
make sure the ipad has wifi turned on.
check the airport express isn't a closed network.
check the airport express to see if mac address control is on.
 
Try updating the firmware maybe too.

I have not had any problem with my airport express.
I would configure it via your Mac/PC and use a WPA key for authentication as well.
Try to use Channel 11.
Also try to toggle it from wireless-n only and mixed mode, n-only might get rid of some bugs in connection.
 
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