Public reports will be available for 30 days upon making them public. Once the 30 days has passed, the link will lead to a dead-end page, indicating that the report has expired. At this point, you must manually reinstate the report's public status in order to receive a new link and restore functionality.
In 8.6, users with an Enterprise or "+ reporting" license type will be able to view reports made visible to them through the client portal. They will be required to log in to view these reports, but you will not have to worry about refreshing public urls.
I hope this helps!