Here's the continuous Direct Mode solution that works for my setup. I'm using a Canon 5D Mark III, Eye-Fi Pro X2, and an iPad 3 (iOS 5).
My original problem was that the Eye-Fi network would connect (displaying the spinning pinwheel instead of a check mark). After about a minute the Eye-Fi network would vanish and I'd be back to my home network on my iPad. What I didn't realize is that I had the Direct Mode settings set to 1 minute (the second slider under Direct Mode tab). I moved that to "Forever", so Direct Mode will stay on indefinitely as long as my camera is powered up. I also went into my iPad settings and switched off "Ask to Join Networks" so it won't switch to any recognized networks I might be around. Ever since then, it's worked great.
So, in short, to use Direct Mode consistently and indefinitely in iOS5:
1.) Complete basic setup via USB, directions: http://support.eye.fi/features/direct/ios-eye-fi-app/
2.) In Eye-Fi Center change Direct Mode "stay" slider to "forever" (the second slider under Direct Mode tab) and click save!
3.) In Eye-Fi Center remove any Private Networks from your card that you might be around
4.) Enable Eye-Fi transfer on your camera if necessary (via settings menu on 5D Mark III, and other select cameras)
5.) Insert Eye-Fi card in camera and shoot a couple photos
6.) Go to Wifi settings on your iDevice and wait for Eye-Fi network to appear (should happen soon after your last picture taken)
7.) Select the Eye-Fi network
8.) Turn off "Ask to Join Networks"
That's it. Should work like a charm after that. Hope that helps