keep widgets in the widget areas

Is there anyway to keep widgets in the widget areas when there is a theme change.

All my child themes are from the same parent theme, and all child themes share the same functions as I have the 1 functions.php in a mu-plugin. So all share same widget areas etc.

From my tests I have noticed that when you install wordpress from the start (multisite or single) and with no edits except to create the child themes, when you add widgets to the widget areas, the widget areas keep the widgets in them when you change themes to start with, then it stops working, and so whenever you change the theme the widgets will appear in the inactivate widget areas, and the widgets will appear back in the widget areas when you go back to the theme that you made the widget changes with.

Thanks in advance