SOLUTION:
There is a security right in Stat that can disable the Delete button under Object Management tab.
1. Maintenance | Security Settings | User Classes
2. For User Class Code = Developer or DBA - highlighted
3. Click on Edit Rights button
4. On the right hand side, look for OraApp Object Mgmt. Expand. Look for OraApp object - Delete Archive Set rights (Enales the user to delete existing Archive Sets of Oracle Application objects). Highlight it and click on the left arrow to move to the left hand side.
5. Logoff Stat Windows Client.
6. Logon Stat Windows Client to verify.