Cam:  This isn't tested, so let me know if you run into troubles with it.
Change sFldr to point to the right place.

Sub RefreshAllFiles()
   
   Dim sFldr As String
   Dim ws As Worksheet
   Dim pt As PivotTable
   Dim sFile As String
   Dim wb As Workbook
   
   sFldr = "\\Server1\MyFolder\*.xls"
   
   sFile = Dir(sFldr) 'get the first xls file
   
   Do Until Len(sFile) = 0
       Set wb = Workbooks.Open(sFile)
       For Each ws In wb.Worksheets
           For Each pt In ws.PivotTables
               pt.RefreshTable
           Next pt
       Next ws
       wb.Save
       wb.Close False
       sFile = Dir 'get the next xls file
   Loop
   
End Sub