What you can do is only set the ToolTip if it isn't already the value you want it to be:
Private Sub AreaLB_MouseMove(sender As Object, e As System.Windows.Forms.MouseEventArgs) Handles AreaLB.MouseMove
ToolTip1.Active = True
Dim itemIndex As Integer = AreaLB.IndexFromPoint(e.X, e.Y)
If itemIndex > -1 Then
Using g As Graphics = AreaLB.CreateGraphics()
Dim s As String = AreaLB.Items(itemIndex)
If g.MeasureString(s, AreaLB.Font).Width > AreaLB.ClientRectangle.Width Then
If ToolTip1.GetToolTip(AreaLB) <> s Then
ToolTip1.Show(s, AreaLB)
End If
Else
ToolTip1.Show("", AreaLB)
End If
End Using
End If
End Sub