I had this same problem with my beloved Apple wireless keyboard and my new, soon-to-be beloved, iPad mini. Could NOT pair the keyboard to the iPad after umpteen tries. What ended up to work for me was a combo of YouTube instructions on pairing the mini with a bluetooth device, and removing the batteries from the keyboard and reinserting them. I don't know just which maneuver did the trick, but the long and the short is that the instructions given in manuals and elsewhere sort of assume you already know what to do, so are not as helpful as they might be.
1) (if applicable) Bluetooth devices cannot be paired with 2 PC's at the same time, and should not even be in range of an initial "paired" computer or device (my keyboard actually re-paired with my MBPro after I'd disconnected it because I'd stayed nearby). On the Mac your keyboard is already paired with, go to Settings > Bluetooth, select the relevant device in the left window, & check "disconnect" from the "performance" button to the right of the "+" and "-" buttons. For good measure, click on the "On" button at top to turn Off Bluetooth on your Mac. "Connected" button in the right window will go from green to red. To be safer yet I shut down my Mac and moved to another room with my keyboard and iPad.
2) Remove batteries from keyboard for a couple of minutes. Reinsert.
3) Turn on your iPad. Go to "Settings" and select "General", then "Bluetooth" (or go directly to "Bluetooth" on the mini). Turn "On" Bluetooth. Press "On" button on side of keyboard and hold for a few seconds. Let go; the keyboard light should start flickering and the iPad should "discover" your keyboard, first as "keyboard", then as "mcgillicuddy's [your name here] keyboard" and start "Searching" (spinning symbol); on the right you'll see "not connected". Here's the part only the YouTube video tells you: click on the box with the keyboard name and the "not connected" message instead of waiting for the cows to come home: you should immediately get a small blue box asking you if you want to pair your keyboard with your iPad [Doh...] and telling you to enter the number 4 digits in my case) listed at the bottom; do this ON THE wireless keyboard, prompthly, and hit "Enter". Presto, your keyboard is paired. If you do not enter the number quickly enough you'll have to click on the "not connected" message again and you'll get the invitation again, with a new number. Hope this helps somebody!
