Things that break a chain (avoid these):
- Using your rollerskates or bicycle
- Encountering a different type of pokémon from the one that you started the chain with
- Encountering a wild pokémon that was not in a shaking patch of grass
- Leaving the area
- Saving and restarting from where you left off
Try using Repels to ward off any non-Radar Pokemon. Slow-shaking grass contain no Pokemon. The same type of shaking will increase your chances.
For more information, look at my source.
Hope I helped!