1. Currently, if the Allow non-admins to create recurring rules permission is unchecked in the More actions > Global configuration.
2. Then, all project members can create recurring rules if they have the view and edit permissions.
3. However, the Project Administrator does not have the required permission to delete those rules, as it requires Admins with the Administer Jira global permission.
4. This makes it difficult and requires lots of intervention from the organization's Admin or site admin to handle those requests.

Suggested feature request
Please grant a new permission for Project Admin to be able to delete the recurring rules in the project that they are the administrator.