My ipad mini shows 66% power but won't charge
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.