This sub will keep the pivot tables 'live.' You could PasteValues over them if you don't want that.
Sub SummarizePivotTables()
Dim wb As Workbook, ws As Worksheet, ss As Worksheet, pt As PivotTable
Dim pasteRow As Long
Const rowsBetween As Long = 1
Set wb = ThisWorkbook
Set ss = wb.Worksheets("Summary")
pasteRow = 1 'first table row'
For Each ws In wb.Worksheets
For Each pt In ws.PivotTables
'change this to TableRange1 if you do not want the page field included'
With pt.TableRange2
.Copy ss.Range("A" & pasteRow)
pasteRow = pasteRow + .Rows.Count + rowsBetween
End With
Next pt
Next ws
End Sub