AIR applications are not permitted to write to the application resource directory. This seems to be a security feature and makes sense, because some systems would not allow to write into this directory at system level.
But for testing purposes you might hack this by using a single line of code:
// Writing into that file would fail var yourFileInAppDir: File = File.applicationDirectory.resolvePath( "yourFile.xml" ); // This is the simple hack: yourFileInAppDir = new File( yourFileInAppDir.nativePath );
But this only avoids a AIR security error! You must be sure to have write access to the directory!