We have seen the same issue. I tested this a few months ago with AIR 3.8. I'm updating to 3.9 now so I'll redo some of these tests, but here's what I discovered at the time:
This issue not only occurs with mobile hotspot connections, but also when a phone call is active and the user switches to our application. In both cases, iOS shows an extra bar at the top of the screen, telling you that you're in an active call or that you have a number of active connections on your personal hotspot. It resizes apps to make room for this bar.
I added a stage resize handler but it does not get called when this extra space is consumed or removed.
In both cases, native text fields ARE relocated when this extra area is moved - so things like Feathers skins are no longer positioned under the native text field.
There appears to be no context loss. This UI can come and go as connections to your personal hotspot come and go, all while you're app is running. iOS appears to dynamically resize the app, but again we get no resize event.
An easy way to test is to enable your hotspot, then while testing over USB, connect and disconnect from your phone's personal hotspot from your development computer. The hotspot status bar will come and go while you're debugging.
If I recall correctly, this occurred in iOS 6 as well.
I was considering adding native code to one of our ANEs to detect when these events occur and calling back in to our app, but not sure that would help since AIR still reports the old stage size throughout these changes, and I'm not sure how much luck we'll have trying to override those values.
Since I'm recompiling our app for iOS 7 compatibility now, I'm wondering if the new transparent status area may allow us to deal with this, since I'm hoping we'll have the entire stage area even when the extra bar appears (though we may still need ANE code to detect when it's there, so we can keep our UI in sync).
Will keep you posted.