I have had this issue since I got my iPad in May of last year.  When I allow the battery level to go below 30% or so, sometimes the device will not charge, even when plugged into the proper A/C adapter.  I have sometimes plugged it in at night, only to wake up and find the battery level at 10%!  Once it was at 1%.
A reset before plugging in the charger seems to fix this.  So now I always do a reset before I plug in the charger.  Once my battery had drained down to 1%, and didn't have enough power to reset.  That time, I was able to plug into a computer USB & charge the device to 4%.  Then I reset it & plugged it into the wall.
I hope this helps someone.