Sounds like you might have more that one problem going on which are sometimes conspiring against you (Swiss Cheese anyone)
Needing to power cycle the charger isn't normal. What happens if you plug the charger in while the socket is off and then turn the socket on? I'd say you've either got a fault on that charger or some circuit protection in the charger or iPad is kicking in to disable the output.
How different are the two sockets? I'd second the advice to have them checked for loose connections - the act of inserting the charger may be causing loose wires to move either in the socket or the legs of the charger.
Do you only have access to one charging cable and one Apple device? Cable problems are pretty common and dirt in the connector can also be an issue. It would be good to eliminate these.