The workspace remembers and restores only which files are open and their (main) windows. Duplicate windows as well as document panes are not remembered/restored. Write an enhancement request by email to IDM if you want an enhancement on window management in workspaces. As workaround I suggest to use a bookmark (with saving bookmarks enabled) to quickly move to the position you want after duplicating a window in the duplicate window after restarting. Or you never close UltraEdit and use the hibernate mode to turn off Windows.
Best regards from an UC/UE/UES for Windows user from Austria