SMS is not guaranteed delivery (part of the GSM standard) and there's no way to verify final delivery, only that the message was initiated by the sender. The mobile phone network will try to deliver for up to 3 days, then the SMS is forever lost to the ether.
I agree with PP and call bull@#$% on the late fee - if the late fees are not explicitly defined in the contract then they can't charge them. I'm fairly sure they need to provide written (as in snail-mail) notice for that sort of fine, too.
Good luck, hope you get it sorted!