iPad charging problem

I am infuriated by a persistent problem with my iPad 4. I put it on to recharge using a genuine Apple cable and mains adapter. I go back later and find that it is no longer charging. I detach and reattach the cable at either end and charging recommences. Later I find the message "Not charging". Over and over this happens. I've tried replacing the cable. I've tried using an alternative 5v adapter. Charging still fails after a while. I put the whole thing in a quiet place undisturbed. The same failure occurs. Any ideas anyone? Thanks.