When 2 records are merged, CRM keeps a link of the inactive record. Because the Alternate ID exists on the inactive record, CRM sees the link and doesn't allow for the ID to be added to the Active record. Delete the ID from the inactive record and add it to the Active one.
Modify the Merge Configuration to keep both target and source's alternate ID's. CRM will move the Alternate ID to the active record during the merge process.