There were indeed a few cheap iphone and iPad cables which would'nt actually charge at all due to one wire being missing (or not connected) apparently, though I thought most of these problems were usually with cheap cables bought from dubious Ebay sellers, I had one myself, dirt cheap, which just wouldn't charge my iPad1, it never even showed the charging icon on top right of the screen.
To the original poster, does your iPad behave the same regardless which 10watt iPad charger your using..IOW I assume you have eliminated a charger fault.
My official iPad charger does charge my iPad3 even when I'm using it, such as when streaming live TV which I use mine a lot for... IOW it's often used as a TV alongside my computer..lol, albeit it will be much slower than if the iPad was powered off of course.
At home.. mine spends a lot of time in a Logitech stand with powered speakers built-in, and I find that seems to charge slightly quicker than the proper 10watt charger, I'm hoping that's not a bad thing. Though in fairness I've used this same stand on my iPad1 for a very long time without any issues.
I have never seen the battery level go down when charging even when the iPad was being used.... so you may have a issue with your iPad (hope not) I would certainly try another charger first if that's possible, if only to eliminate the charger.