Applying a template to a sub-project clears the Parent field
Please see the difference between template headers when creating a project.
1. The Template header 'To create a project from a template click here' which is displayed before you create a project implies that irrespective of the details given earlier, a new project will be created with the corresponding template data.
(Which will wipe out fields such as "Parent".)
2. The Template header 'To apply template click here' which is displayed after a project is saved/created is meant to be used when applying a template to already created project. ( And this link is visible as long as no project tasks are created.)
Hence, While creating a subproject - In order to preserve field values when applying a template, the project should be saved first and then the template should be applied.