I must say, I have this same issue... I'm pretty sure it's the app I use (Nanostudio, a music app that uses lots of cpu resources, but still, it's frustrating.)
Anyway...I find that using the iPad while plugged in (with the power adapter that came with the unit, nothing wrong with my outlet, and my brightness is always lingering around 50%) and still the battery will drain while it is plugged in.
I have absolutely no other issues with the iPad, the screen is great (no yellow or pink, at least if there is, I don't notice it, and no backlight bleeding,) and everything works perfect as far as iOS. I'm assuming this is just something I have to live with when using certain apps/game that use so much cpu power but it's the only device I've ever owned that drains battery when plugged in.
If I bought a larger wattage 3rd party charger, do you think that would solve the issue?