Depending on the state you live in, he has to give you a certain amount of notice ahead of time. I have lived in apartments where they inspect them annually but never any more often than that. It seems unreasonable and quite possibly illegal to inspect every month.
The law in most places is that he has to notify you of his visit ahead of time before coming into your home. If I knew what state you were in I could tell you the exact laws and whether or not he is breaking them.