Q:

If my Pokemon faints, does it break my chain?

I was shiny hunting in ORAS using the DEXnav, and my Pokemon is close to fainting.
If my Pokemon faints, does it break my chain?

A:

Chaining with DexNav in ORAS is not broken by your pokemon fainting.*NOTE
Per this reddit thread (formatted for clarity)
What will break my chain? 
- Encountering other Pokemon WHILE NOT SNEAKING. (Use repels) 
- Leaving the route. 
- Running from battle. 
- Scaring off a Pokemon.

This is also supported by Bulbapedia
*NOTE: If it is your last/only pokemon that faints, you will be sent to the pokemon center, which breaks the chain due to leaving the route.

