I'm having a hard time finding clear information on the situation about deploying Flash with air runtine on iOS. While it seems clear that the plugin flash for iOS is ended I didn't find any infos about Adobe AIR. Is it still possible to distribute apps for iOS through the iTunes Store. Arte the apps using Air still running on iOS.
While it seems clear that the plugin flash for iOS is ended
There was never any Flash plugin for iOS. Apple has always been very forward about iOS simply does not support Flash. It ended for Android.
Adobe AIR apps compile down into native code (ARM for iOS). You're not actually running "Flash" or "AIR" at that point. This method of deploying apps is very convenient because the same code used to produce an AIR for iOS app can be largely re-used on the Android side, reducing overall costs involved in developing for both platforms.
I think it's pretty safe to say this method of app creation isn't going away anytime soon.
Lastly yes there are plenty of AIR for iOS apps on the market (I have some myself) and they all work fine as long as you do as an Xcode or Java developer would when a new OS comes out. You test for compatibility and update as necessary to keep your app functioning properly. The vast majority of fixes needed come from OS changes, not issues with Adobe AIR. Stability is very good.