FYI automatically clears and refreshes the search criteria when you leave a screen or when you logout.
However, if you have Sticky Views set as "On, when you select a particular view in any list (Client, Jobs, Tasks or Documents) that choice will be your default until you select a different view. If a search criteria has been included in the view, this will also be retained so in some cases the search criteria will follow you throughout FYI. Refer to Sticky Views.