As Desdenova pointed out, the array you are trying to add is nil, so of course the content you add to user defaults will also be nil.
You need to add a valid property list object to user defaults. Nil objects, or objects that are not property list objects will not save.
If you think self.FlipsideView.myMutableArray should be non-nil, you need to go trace through the code that creates and populates that array.
If the property is declared as weak or unsafe_unretained that is your problem. It's getting deallocated.