When adding or editing a custom label field, if you change the ‘Allow Empty’ option to off, any changes made will be ignored and lost without warning when you save.
Perhaps this is due to existing items not having a label set, so not allowing that to be empty causes a problem. Maybe ‘Allow Empty’ should include a default value to use for cases where no label has been set. Maybe even give each value a check box to be ‘Default’, then if ‘Multiple Selection’ is enabled, multiple default values could be assigned to items that have no label already assigned.