How old is the ipad? Sounds to me like the battery is just knackered. They don't last forever. Leaving it permanently on charge isn't a good idea. Batteries can only be charged so many times so best practice is to use it until it's really low then charge it to full. Rather than keep topping up if you see what I mean.
My wife has knackered her laptop battery by leaving it permanently plugged into the mains. I take my battery out of my laptop since I rarely actually travel with it. That way i'm not damaging it.
Do you have a lot of apps open? My kids leave apps like pvz and angry birds on and it really drains my batteries. If you double click the button any open apps will show up at the bottom of the screen and you can close them by keeping your finger on one and waiting for them to jiggle and show a red cross. If this doesnt help I'm not sure what to suggest. Hth.
My iPad battery seems to be losing its ability to hold onto charge - I used to be able to take it off charge after lunch, and it would last easily all afternoon and evening, and then went back on charge at bed time. But now it can't get through the whole of the evening before needing to go back on charge.
Ds2 says this is because I have been leaving it on charge once it is fully charged (because it was charging over night, and then getting left on charge until the afternoon), so I have knackered the battery.
He says there is nothing I can do to reverse this damage - is he right, and if he is wrong, what can I do to boost the battery life on the iPad?