Thank you for the response. Double-clicking on the column certainly works ... but only for a single-column sort.
Perhaps I'm not describing my problem correctly.
When I'm displaying information about a table, there are a number of tabs displayed: columns, data, constraints, etc. Selecting the data tab causes the rows of the table to be displayed along with a sort button and a filter space. That's the sort button I'm describing in my original post. When I click on that sort button, a pop-up screen appears: "Sort Columns". This works fine for all my tables except one! For one table the Sort Columns pop-up does not appear, so I'm unable to do a multi-column sort on the data display.
As I mentioned in my post, when I copy this problem table into a new table, I'm able to accomplish the sort, but not on the original table.