I've had problems with table edge cases such as when a table is the first thing in a document. The consistent way I get around it is to use Word's insert caption which seems to avoid that issue and may well also work on your butted tables. I can't produce two butted inline tables without them merging - perhaps you are floating your tables?
In any case, try this approach which may work with your doc.
Code:
Sub aTest()
Dim oTable As Table, oRng As Range, oFld As Field
For Each oTable In ActiveDocument.Tables
Set oRng = oTable.Range
oRng.InsertCaption Label:=wdCaptionTable, ExcludeLabel:=True, Position:=wdCaptionPositionBelow
oRng.InsertCaption Label:=wdCaptionTable, ExcludeLabel:=True, Position:=wdCaptionPositionAbove
Next
For Each oFld In ActiveDocument.Fields
If LCase(oFld.Code) Like "*seq table*" Then oFld.Delete
Next oFld
End Sub