Good call, I was not aware of the Exceptions ANE (and thanks Distriqt for making it available for free 😉 )! I hope you'll receive useful information from it. I'd be glad to add it to my apps, but I'm currently revamping them with the Distriqt ANEs, and I'm in the middle of many changes, so I won't be able to publish them immediately.
Actually, I don't have consistent behaviors. To sum it up, my 2 most recent apps are different: there is one which is pretty simple (https://play.google.com/store/apps/details?id=air.com.indiegoes.angelnumber) and another one which is more complex (https://play.google.com/store/apps/details?id=air.com.indiegoes.oraclecards). Until recently, I had Signal 11 errors in both.
I also have about 27 apps built with AIR 27-28 and targeting Android SDK 19. None of them have Signal 11 errors.
I republished my 2 latest apps with AIR 184.108.40.206, targeting Android SDK v23. Now, after a few days, I still get Signal 11 errors in the complex one, while errors seem to have stopped in the simple one (for now at least).
So yes, the webview might be the problem, as Michael suggested earlier. I think I could re-implement the display of my web page in another way (I could re-create it with display list elements). However, it would not really explain why my simpler app, which doesn't use a webview, had errors before I targeted a lower Android SDK. I use some custom web services in both though, I don't know if the URLLoader class in AIR uses some native network features on Android that may cause issues. There may be several elements converging, it's still difficult to know.
Do you have means to remove this webpage display in your app, and see if it solves your issues? Or is it a mandatory feature?