It's not necessary to break the chain. It's just wayyyyyy too hard.
Shiny hunting in caves, Mt. Pyre, and water routes in ORAS is hopeless. Don't try it. The Pokemon do indeed get much faster and almost impossible to reach every fifth encounter. It was one of the most criticized aspects of the whole game(s). I would not recommend shiny hunting for Sableye. You're better off looking for something like Luxio (one of my favorite shinies) that I've had success with.
I'm sure if GameFreak thought twice about this, and look back at it now, they regret doing this.