The network slicing concept (probably one of the most important innovation brought by 5G) promises significant flexibility and autonomy for network management. Thanks to its main key features, heavily relying on the NFV and the SDN technologies, new communication services can be designed and deployed much faster than before. However, maintaining the reliability level of conventional networks remains a major open problem. One of its consequences is that the monitoring of the network infrastructure dedicated to this class of services is an essential challenge, which we address in this paper. In this paper we describe a new monitoring procedure, customized for NFV-based network infrastructures deployed with the Service Function Chaining (SFC) mechanism, one of the most important key enablers for NFV networks. Our solution allows the deployment of efficient probing schemes that guarantee the localization of multiple simultaneously failed nodes with a minimum cost. This is formulated as a graph matching problem and solved with a max-flow approach. Simulations show that our solution localizes the failed nodes with a small rate of false positives and false negatives.