Your bank and the Post Office act on your behalf when transmitting the funds. If they delay, you are the one who has to take the consequences.
On the other hand, your landlord cannot blame you for its own lack of diligence in logging your check. You would, however, have to show that it received the check in a timely way. You could do that by showing when your bank mailed it and showing that delivery had never taken as long as your landlord said it had, before.