I'm having a similar issue. I've had the iPad since last Sunday and have charged it overnight everyday. It came to the weekend (where I tend to use the iPad more), the battery ran down yesterday early-afternoon while I was watching video so I decided to recharge it using the 10W wall charger.
I then read a Kindle (iPad app) book for hours yesterday afternoon (really easy to do on the retina screen) with the charging cable still plugged in, but even though the charging symbol was present - when I took the charging cable out to see what the battery was like, it hadn't moved (up or down)!
I made a Genius appointment today, the guy did a diagnostic and couldn't find a problem with the battery, he said it was "healthy". He offered me a replacement iPad for peace of mind, but thought maybe there will be a software update soon to fix the issue (I opted to keep my iPad since I'm not convinced a replacement will be any different).
My thinking is the same as a few people here, I'm wondering if the 10W adaptor is really cut out for the new power hungry battery.
Every battery-included electronic device I own is capable of recharging while in use (including my £20 shaver). If it's design flaw then I expect this to be fixed, partly as this costs so much more, but mostly as it's going to become a real inconveniece. I hope that adding to this board might help surface the extent of the problem.
Otherwise, I'm loving my new iPad!