On a particular Project, there is a related list (Story -> Project) that will be visible on the project form as Stories and then disappears when the page fully loads.
Even though "Story -> Project" related list is added from the available slush bucket to selected bucket, it continues to disappear.
This is due to "Execution Type" on the Project/Projects.
If the Execution type is "Waterfall" then the Related list is hidden by the Client Script: "Hide Related List on Execution Type"
When the Execution type for Project is Agile or Hybrid the Story -> Project related list should be available on the Project.
To view the Client Script:
1. Navigate to System Definition > Client Scripts
2. In the name column, search for "Hide Related List on Execution Type"