iPad refusing to connect to Airport Express

Hello.

I have an iPad (64GB 2012 retina model with wi-fi and cellular, running 6.1.3) which I am suddenly having difficulties connecting to my Airport Express (mid-2012, with a 2.4Ghz and a 5Ghz network, running 7.6.3). I was having the difficulties prior to updating to 6.1.3, and they persist afterwards.

My two MacBook Pros, one iPad (a 1st generation iPad running iOS 5) and one iPhone (running iOS 6.1.3) all connect without any difficulties.

Suddenly, today my iPad began to refuse to connect to the network, to which it was formerly happy as Larry to join. It coincided with an internet outage, which was fixed by cycling the router.

Here's what I've tried:

Restarting the Airport ExpressResetting the Airport Express and rebuilding the network, with new passwords and new network nameForgetting the old network on the iPad, and inputting the details manuallyResetting network settings on the iPadConnecting to the 5Ghz and the 2.4Ghz networks

The iPad can 'see' the network - the name is listed next to the Wi-Fi icon in settings, it tries to connect, accepts the password and so on. But the spinning wheel next to the network name in Wi-Fi/Choose a Network keeps on spinning. When I look at the connected clients, the wireless clients listed don't include the iPad wireless card address.

I can connect the iPad to my iPhone via Personal Hotspot, or to my MacBook Pro if I enable internet sharing. I haven't access to another network to try connecting to that.

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