Inserting something into a range can be problematic when it already has content.
Try defining a range and then collapsing that to a specific location
Code:
Dim aRng As Range
Set aRng = ActiveDocument.Range.Tables(1).Cell(2, 2).Range
aRng.Collapse wdCollapseStart
aRng.InsertCrossReference ReferenceType:=wdRefTypeBookmark, ReferenceKind:=wdContentText, _
ReferenceItem:="DATE", InsertAsHyperlink:=True