This is best achieved by making a document object of the source document, and iterating through your new documents also as document objects. That way you can transfer over the margins directlly.

BTW: your source document uses Word poorly. No styles; extra tabs and paragraphs.
[vba]
Sub SplittingDocumentIntoPages()
Dim SourceDoc As Document
Dim PagesDoc As Document

Set SourceDoc = ActiveDocument
' Used to set criteria for moving through the document by page.
Application.Browser.Target = wdBrowsePage

For i = 1 To SourceDoc.BuiltInDocumentProperties("Number of Pages")

'Select and copy the text to the clipboard.
SoiurceDoc.Bookmarks("\page").Range.Copy

' Open new document to paste the content of the clipboard into.
Set PagesDoc = Documents.Add
Selection.Paste
' Removes the break that is copied at the end of the page, if any.
Selection.TypeBackspace
DocNum = DocNum + 1
PagesDoc.SaveAs FileName:= _
"H:\My Documents\Abrechnung_" & DocNum & ".doc"
PagesDoc.Close
Set PagesDoc = Nothing
' Move the selection to the next page in the document.
Application.Browser.Next
Next i

End Sub [/vba]Notice I removed the ChangeFileOpenDirectory. Firstly, it is not needed, and secondly it is inefficient to have a change insruction through each and every iteration of i.