The Software Defined Networking (SDN), an efficient network technology, allows researchers to program their networks to meet different application needs. In this paper, we focus on failure detection services in multiple SDN controllers. We review some classical failure detection services and discuss how these services work. These classical failure detection services have the high mistake rate problem. To deal with this problem, we propose a failure detection service with low mistake rates (FDLM) mechanism. We use a modified gossip protocol to distribute heartbeat messages and have multiple controllers to make failure decisions in order to achieve low mistake rates. Experiment results show that the proposed FDLM has better performance in terms of average mistake rate, 95.5% (79.8%) lower, compared to Akka under message loss for the case of four (three) controllers. The significance of achieving low mistake rates in the proposed FDLM is decreasing unnecessary SDN controller failover, which causes overheads of reelecting a leader controller, restarting a controller and synchronizing the restarted controller with the leader controller.