When automatic mode is enabled and issue is state has been changed to "Closed" state work time is not logged.
Plugin (user Automated Log Work) needs following permissions set per project to work properly:
Use Permission Helper to check if appropriate permissions are set
"Closed" state property "jira.issue.editable" is set to "false"
This means that JIRA forbids to edit (also add "Work Log" ) for an issue in the state.
https://confluence.atlassian.com/jira/allow-editing-of-closed-issues-138704.html