The code I posted works for the selected table, whether or not the table is at the start of the document. If you want it to work for all tables in the main story range then
Code:
Dim oTable As Table
Dim oRng As Range
Dim i As Integer
For i = ActiveDocument.Tables.Count To 1 Step -1
Set oTable = ActiveDocument.Tables(i)
Set oRng = oTable.Range
oRng.Collapse 1
oRng.Select
Selection.SplitTable
Set oRng = oTable.Range
oRng.Collapse 0
oRng.InsertParagraphAfter
DoEvents
Next i
Set oTable = Nothing
Set oRng = Nothing
If you have an example of tables it doesn't work with, post the document so we can evaluate the problem.