If you have a different wild encounter during the chain, then it will break. If you run from the Pokémon, then the chain will break.. ~ Serebii
This basically sums it up. Your chain will break if you encounter a Pokémon other than Absol, if you run away from the encounter, or if the Pokémon escapes or is scared away. Also, leaving the area (Flying/Soaring away, walking onto another route, or entering a Secret Base) will also break the chain. Be sure to bring plenty of Max Repels to avoid encountering other Pokémon, as well as some Elixers/Ethers/Leppa Berries and Max Potions/Full Restores so that you do not need to leave the area in order to restore. Good luck finding Shiny Absol!