The Apple adapter will actually trickle charge the iPad just enough so battery doesn't deplete while used with iTwo or iOne. It's not enough to show the charging icon on the iPad but just enough to keep the charge at a sustained level while in use, and when it's not in use will slowly charge the iPad.
We've done recordings with the Apple 12W adapter and an iTwo with 2 Mics for 3+ and 4+ hour recording sessions without issue on an iPad without issue. However we did optimize the iPad to accomplish this performance. The power draw of an iOne or iTwo may be aggravating other apps that are already pulling data which requires power to operate in the background.
Take a look at what other applications you may have running that are already pulling / sending data in the background, apps like Skype, or any number of free games that may be installed, or any (free?) game. Even while the iPad is idle and the applications are merely installed and not running, they are still sharing your computing power via your wi-fi connection.
For best performance for running any audio app on iPad with iTwo, iOne (or anyone's interface for that matter with an iPad) would be recommending to enable Airplane mode and dulling the brightness as needed.
This will ensure top performance for your audio project especially if you're running on a battery pack or in an area where reliable power is questionable.