Symptoms

Worklist filters for the Sharepoint 2013 Web Part do not save filters when navigating away from the site containing the web part.
 

Diagnoses

This occurs because by design currently the Sharepoint 2013 Worklist Web part does not support this functionality of persistent filters.
 

Resolution

A workaround for this is to create a form and use the Worklist control for smart forms, personalize filters on the control, add a smartform viewer for sharepoint onto the page, and then display the form using the viewer on preferred sharepoint site. When changing the filters on the Worklist control at design time, these filters will be automatically saved. Users may still enter new filters at runtime when viewing the worklist through the smartform viewer for sharepoint but, these will not be saved when navigating away from the page.