Earlier quoted context omitted.
It is, or should be, your responsibility to notify them when payment it due.
Ah, but there is no indication they didn't. What happened is that the check was sent, but did not arrive. In other words, the customer and his agent (the postal service, probably) in the exchange did not fulfill their job of getting the money to the business. That is not something the business can control, and if you try to make it their responsibility, they will simply start refusing payment by mail, since it would…
In any case, I read this as the notice that payment was required is what got lost, not the payment itself.