To avoid adding to the comment chain, I'll just write an answer.
As I said in my comment, most AIR devs avoid using SharedObjects for various reasons. They are limited to ~100kb, you have no control over them, and apparently are flushed on iOS.
With that said, most AIR devs prefer to use File and FileStream which give you direct control over the device's file system.
FileStream features a method called writeObject() which does exactly what you want. Say you have the following strongly typed objects you wish to save (note: only public properties are saved to disk):
var a:Class1 = new Class1();
var s:Class2 = new Class2();
var d:Class3 = new Class3();
var f:Class4 = new Class4();
You'll want to combine them into a single object, or save them individually. For this, I will combine them into a single object.
// you could also use an array, or any other object, to do this
var obj:Object = {objA:a, objS:s, objD:d, objF:f};
Then you want to use File, which is a reference to a file or directory in the file system, and FileStream, which is what communicates with the file system, to write the object.
var f:File = File.applicationStorageDirectory.resolvePath("prefs.conf");
var fs:FileStream = new FileStream();
fs.open(f, FileMode.WRITE);
fs.writeObject(obj);
fs.close() // NEVER forget to close()
And that's it.Your objects are now saved to disk. You can open them using File and FileStream again.
fs.open(f, FileMode.OPEN);
var obj2:Object = fs.readObject();
fs.close();
obj2 will have the same properties as obj and they will match the objects you originally saved. It is worth noting that these objects will not be of the same type as your custom objects. Unless they are primitives (Object, Array, String, Number, int, uint, maybe a few others), every object that is read from a Byte stream (whether it be ByteArray, FileStream, URLStream, etc) will be typed as a standard Object. You can get around this with registerClassAlias(), however.
EDIT: As a quick note, on iOS, you should always set File.preventBackup to true if they are anything other than preferences. Apple will reject it otherwise. The good news is, though, that those settings should be backed up to iCloud and persist between installations.
SharedObjectis generally avoided in AIR development in favor ofFileandFileStream. SharedObject has a 100kb limit, which really only makes it good for saving settings. And, even then, I personally preferFilesince I get more control over it. - Josh