UPDATE: I have replaced the flash module in the header position with a simple jpg image, which now shows on the sub (child) menu items. This is a suitable work around for me at this time. However, it still might become a future issue if flash modules only work with parent menu items and not the child menu items.
My header module only shows on top level menu items. It disappears on all of the drop down items. I do have the header modules menu assignments properly selected.
Any suggestions? Site Link