Results of Saved Searches can be saved into Excel sheets using a predefined template (see: Upload Saved Search Results Template). By default, when creating an Excel template sheet, values are not automatically updated.
Example: I have created a series of Task Saved Searches for which I have created an Excel template to download the search results into. I have two additional worksheets in the xlsx file that perform some basic math on the search results data. I can upload the template and download the results, but the formulas on the additional worksheets will not update with values from the Search Results worksheet without forcing a manual update
This article describes how to automatically update values.
To automatically refresh data when a workbook is opened:
Click any cell in the external data range.
On the main menu's Data tab > Connections group, click the arrow next to Refresh and then choose Connection Properties.
Go to the Usage tab.
Under Refresh control, enable the Refresh data when opening the file check box.
To automatically refresh data in a PivotTable:
Right click on your PivotTable.
Choose PivotTable Options... from the contextual menu.