That is because a referenced cell change doesn't trigger the change event
for monitored cells. It can be circumvented by using the Calculate event to
trigger the code for any change, not efficient but it works

Const WS_RANGE As String = "H1:H10"

'-----------------------------------------------------------------
Private Sub Worksheet_Calculate()
'-----------------------------------------------------------------
Dim cell As Range
   For Each cell In Range(WS_RANGE)
       Call ColourMe(cell)
   Next cell
End Sub

'-----------------------------------------------------------------
Private Sub Worksheet_Change(ByVal Target As Range)
'-----------------------------------------------------------------

   On Error GoTo ws_exit:
   Application.EnableEvents = False
   If Not Intersect(Target, Me.Range(WS_RANGE)) Is Nothing Then
       Call ColourMe(Target)
   End If

ws_exit:
   Application.EnableEvents = True
End Sub

'-----------------------------------------------------------------
Private Sub ColourMe(ByRef Target As Range)
'-----------------------------------------------------------------
   With Target
       Select Case .Value
           Case "Open":
                   .Parent.Cells(.Row, 1).Resize(, 10).Interior.ColorIndex
= 3  'red
           Case "For Review / Approval":
                   .EntireRow.Interior.ColorIndex = 6    'yellow
           Case "VerifiedParent.Cells(.Row, 1).Resize(, 10)"
                   .Parent.Cells(.Row, 1).Resize(, 10).Interior.ColorIndex
= 5    'blue
           Case "Closed":
                   .Parent.Cells(.Row, 1).Resize(, 10).Interior.ColorIndex
= 10   'green
           Case "Pending":
                   .Parent.Cells(.Row, 1).Resize(, 10).Interior.ColorIndex
= 38   'rose
           Case "Rejected":
                   .Parent.Cells(.Row, 1).Resize(, 10).Interior.ColorIndex
= 37   'pale blue
       End Select
   End With
End Sub