Using the battery level meter in this manner is comparable to using your car's fuel gauge to calculate miles per gallon. The only thing that matters is the total amount of operating time from full charge to auto-shutdown.
Use the wall-mount charger that came with the iPad and charge overnight. Admittedly the labeling is hard to read but, if you use a magnifier and squint your eyes, you'll see "Output 5.1V, 2.1A." The symbol between volts and amps is the symbol for DC. Do NOT use an iPhone charger. Do NOT use an iPod charger. Do NOT use a computer's USB port. Then, operate it normally until auto shut-down (ignore any low level alerts that may appear). An irony is that doing that test to determine the total operating time is also the exact procedure necessary to calibrate the battery level meter.
I'm not claiming that you do not have a problem. I am stating, however, that we don't yet know whether or not a battery problem exists.
Use Your iPad Regularly
For proper reporting of the battery’s state of charge, be sure to go through at least one charge cycle per month (charging the battery to 100% and then completely running it down).
Elsewhere, Apple elaborates and explains that two half-discharges (or four quarter-discharges, etc.) equals one full discharge.
Try restarting your iPad by holding down the on/off and the home buttons at the same time until you see the Apple logo. Then try charging it. If you are still having problems try conditioning the battery. Take a look at this link, http://www.apple.com/batteries/ipad.html