Thanks, I will see if I have time to do a test site.
I have tried changing the order with both the up arrow and down arrow in the list of categories and with the dropdown menu when editing a particular category. Nothing I do changes the order of the subcategories.
Aha! I just discovered something. Actually, when I select the front end option to "Show subcategory:", the subcategories are in proper order in the list that shows all the categories. In other words, the "tree" view works - Categories and subcategories all in their proper order.
However, when I click on a Category and it lists the subcategories, then the view is no longer in order, whether or not I have the "show subcategory" option chosen or not.
I also should not that I have a menu item that links to a subcategory. Here, as well, the subcategory is not in order.
So it has something to do with the subcategory list, alone.