My iPad mini shows 66% power but will not charge. Is there a power level it must drop to so it can charge? This true fromAC or USB.
to answer one of your questions, No. you should be able to charge your iPad (or any iDevice) at any time.
Second, eliminate your wall unit as a variable. Try another iPad charger and see if it charges.
(note, USB 3.0 ports on Macs seem to be able to charge iPads, but I haven't discovered a PC port that will actually charge an iPad, don't rely on USB for diagnosis)
Finally, the iPad mini came out late last year right? It's still under warranty, back up if you can and setup an appointment at the apple genius bar and they'll swap out whatever item is not functioning for free.
make sure that you provide enough current (especially if its a newer Ipad) My ipad 3 needs 1000mA otherwise it will not charge.
Which practically means that if you use a charger for an older i-device it will not charge . You need to charge it with a newer charger (the one that came with it preferably or one that provides 1000mA)