A similar issue happened to me recently. Only instead of the keyboard, it happened with the menu bar after playing with the native video player (called through a stageWebView) on an iPhone. My app's screen was "pushed down" by the menu bar after accessing the video controls in the iOS app-switcher bar (double-tap home button and swipe all the way to the left).
It was a rather remote circumstance involving a video being "AirPlay-ed" in the background, but I do suspect a related issue going on here with AIR (3.2) not playing well with native iOS controls.
you can use <softKeyboardBehavior>none</softKeyboardBehavior> setting in your xml description file.
none - will not move the application
pan - will move the application up
Yes, I finally used <softKeyboardBehavior>none</softKeyboardBehavior> and making my own panning, kind of:
-move stage where tapped textfield is visible
-move stage to y=0
Getting input textfields to work consistently in Flash has been allways a PITA (I allways remember the well-known bug FP-40 and its many variants), but getting the iOS soft-keyboard into stage makes things much more funny
For my needs, if you wanna know, I finally sticked using a out-of-view StageText (which is the only one receiving "some" KEY_UP events) and a dynamic textfield with a fake blinking cursor to let the user know what's going on while he's typing (appart from panning myself).