Why are you looking for a solution other than "don't replace your rootviewcontroller". That is the correct guidance. It is not a bug in iOS. In general, you should not replace the root view controller.
It sounds like what you really want is a third view controller to serve as the root view controller of the window and manage the Main and Entrance view controllers as children. Try that and also brush up on using View Controllers, and if you run into trouble we can try to help.
View controllers are designed to work in very specific ways and if you misuse them you'll experience all sorts of undesirable effects. Sometimes you'll get away with it at first, by rest assured, down the line, it will come back to bite you.