Usually this happens because both alumni accounts have an Alumni Affiliation tied to them. The system prevents duplicate Alumni Affiliations on one account. To merge these accounts, you'll need to remove the alumni affiliation from the new account by going to:
  1. Core > Users > Edit User Profile Data
  2. Search the new alumni account you want to remove under Potential Duplicate Users
  3. Under System Information, click Alumni Affiliation
  4. Edit
  5. Delete
  6. Save
Now you will be able to go back to Potential Duplicate Users and merge these accounts without issue.