The code might fail under some circumstances. Would suggest this small change... See the code in red...

Code:
Private Sub CmdBtn_Click()
    Dim num As Integer, date1 As String, date2 As String

    ActiveSheet.Unprotect

    date1 = Trim$(LblDate1.Caption)
    date2 = Trim$(LblDate2.Caption)

    If date1 = date2 Then
        num = Application.CountIf(Columns("D:D"), date1)
    Else
        num = Application.CountIf(Columns("D:D"), date1) + _
        Application.CountIf(Columns("D:D"), date2)
    End If

    LblNum = num

    ActiveSheet.Protect
End Sub