I'm having a similar problem, in that my iPad will not recognise the eye-fi card wifi network.
I have the latest card firmware (brand new card and updated on initial setup), and I have the latest version of the iPad app.
I have disabled any other networks on the card, so the only option is direct mode.
When I put the card in my camera (Canon t3i/600D) and take some photos, no eyfi network appears on my iPad, even after several minutes.
I have been able to get the eyefi network to appear, but only under the following circumstances: when the card is not in the camera, but plugged into the computer using the USB adapter. Just being powered up via the USB alone is not enough though. When I fire up eyefi centre and go into "direct mode settings" and click "start direct mode network", then the eyefi card network is detected by my iPad. However, as soon as I unplug the eyefi card from the computer to put it back in my camera to take some more shots, the network disappears and I can't get it back again until I plug the card back into the computer and select "start direct mode network" again. I'm tethered to the computer - which completely defeats the purpose of being mobile with the iPad (the reason I bought the card!!)
Incidentally, the app seems to be working fine because whilst the card is in the USB reader and I have started the direct network, the iPad app loads all the recent photos I have taken (quite promptly). But again, as soon as I remove the card from the USB reader to put it back in the camera, it all falls apart.
PLEASE HELP!! I'm tearing my hair out trying to figure out what on earth is going wrong!!