Recessed lightning connector - poor connection fixed.
Look carefully at the bezel & connection of the lightning connection port in the edge of your iPad (or iPhone) *if it has a curved edge* in the design. After taking our iPad2 to the Apple Store and a 3rd party store, they said it was un-fixable and no one would touch it, nor realized why it was barely connecting - and relying on being propped up at a funny angle with only one cable that seemed to work with it...sometimes.
After buying a new iPad (as that one might have stopped charging any day), I looked at it closely again this month and tried one last cleaning attempt with little swabs and ISO-propanol alcohol. No luck.
Then I realized that its bezel seemed recessed from the edge a little bit - and I compared the only cord we had that worked to other cords: the sometimes working non-apple cord had the connection points just a little further away from the plastic collar, deeper in - and that was why it could be connected. The lightning port had somehow been recessed maybe 1 mm or less, from a drop, or, more likely, from us pushing the charger cable in too hard to desperately try to make it connect. The top (glass side) edge of the curved edge of this model was hitting the lightning cable collar and restricting it from going in deeper. Carefully pressing the plastic against a grinding wheel changed one side to a 45 degree angle quickly and easily, and now, it goes in as deep as it needs to ...and connects 100% every time, no wiggling or propping against the wall needed! Fixed.