If they feel it is unsafe for them to deliver your mail because of your dog they have every right to refuse to deliver your mail. There seems to be a misunderstanding about that. My husband is a Postal worker and delievers mail and he has had over the years dogs come at him and he has refused to deliver their mail, until the problem was fixed. Just yesterday he had a dog break through a glass window to come at him. It is nothing personal against you or the dog, it is for safety reasons. We just had a mail carrier about a month and a half ago, Got his face dang near ripped off due to a dog. Carrier safety is more important, so please put your dogs away, make sure your fences are locked ect.
God Loves you and So do I.