I did the Louis quest again on my latest character, but this time I chose to blackmail him into letting me keep frost.
He still stands outside Whiterun all day and all night, but he has not been duplicating and its been 50+ hours since I did this quest. (I had 6 of him on my previous character in about the same time frame)
I'll assume that the duplication occurs when you let Louis run off with Frost (That's what I did the first time).