it seems to me the adapter is the culprit.
I think the iPad mini tell the charger to stop charging, thinking it had reach 100%. So the charger stop. So you plug to iPhone 5 also will not charge. So once you power on and off the charger, it reset, so it start to charge again. I maybe wrong on this. I did not try to plug into my iPhone 5, but I do power On and off the charger while the cable is still plug into my iPad mini, still will not charge until I reboot my iPad mini, then it start to charge again. This may have something to do with the wrong reporting of iPad mini battery status which can be say battery calibration issue.
