It's really peculiar: It turned out, that the finally "oTextNode.Rewrite() " prevents the sub text elements from being changed. If this line is left off, the sample works for me!
If (oEle.IsTextNodeElement) Then
Dim oTextNode As TextNodeElement = oEle.AsTextNodeElement
Dim oText As TextElement
Dim EleEnum As ElementEnumerator = oTextNode.GetSubElements()
If (EleEnum IsNot Nothing) Then
Do While (EleEnum.MoveNext)
oText = EleEnum.Current
oText.Text = "New Text"
oText.Rewrite()
Loop
End If
' oTextNode.Rewrite() ' **** This prevents the sub text elements from being changed !?
End If