Checkride failures are taken in context. The recency of the failure, number of failures, cause of the failure, and how you responded to it are all considered.
It is not uncommon to have busted a checkride, especially one of the CFI rides. I would say having more than 2 on your application may make it hard to get called for the interview and given the chance to explain the failure. If the application asked about the failure and gives you a spot to enter remarks do so. Keep the remarks about the failure brief and how you over came it.
In the interview be sure the own the failure and be able to tell them why you failed the ride and how you learned from it. After that the ball is in there court. You can even bust a 121 checkride and still get hired by a major. It's just all in the details of the failure.