Wow a month old and 100% completely trained! His name should have been Miracle!
Sorry but I don't agree with rubbing his nose in it. Dogs noses are super sensitive and I think that could do more damage than good, not to mention it's rather cruel. When human children have accidents their noses aren't rubbed in it, I don't think it is necessary to do that to a puppy either.
Try crating. Get a crate just big enough for the puppy to stand up and turn around in. Put him in it for awhile, then take him straight outside, give him time to do his business and when he does praise the dickens out of him. If he doesn't do his business, put him back in the crate for a bit and try again.
That's the way I trained a litter of 8 pittie pups, they were fully house trained within a week, mind you they were slightly older than a month old.
Abigail~ APBT~ 2
Jersey ~ APBT~5(ish)
Kato ~Rottie~ 5&1/2
Wendellan~ Feline~ 10(ish)
"Da-Goob"~ APBT/Dogo x (5-6ish)
"My Pitbulls are better behaved than your kids!" (my favorite bumper sticker)