In the DeskPack Ink Manager (part of the Esko Data Exchange plugins), the order of the inks cannot be changed by dragging an ink entry up or down in the list.
Symptoms
Click an ink in the Ink Manager and try to drag it to a new spot in the list, nothing happens.
Solution
First, if the Ink Manager palette is docked to another palette try moving it so it is separate (undocked) from any other palette.
If this does not help, then the Adobe® Illustrator® workspace may be corrupt. Most of the time, a custom workspace is being used and this sometimes gets corrupted after docking/undocking of palettes.
To resolve the issue, you'll need to delete the complete Adobe® Illustrator® CSx Settings folder in ../Library/Preferences.
See this article for more information on how to delete the preferences folder: