Wireless Sensor Networks (WSN) are used in various critical monitoring applications such as military safety, environmental surveillance, etc. In such scenarios, it is common that WSN nodes are threatened by potential adversaries. Since the network lifetime is known to be the one of the most important performance metrics in WSNs, capturing the most critical nodes and incapacitating these nodes by various attacks may significantly reduce network lifetime. WSN lifetime reduction due to the elimination of the most critical sensor node set has never been investigated in the literature. In this study, we proposed two Linear Programming (LP) based algorithms to analyze the impact of capturing multiple critical nodes on WSN lifetime through numeric evaluations. Our results reveal that capturing the multiple critical nodes in WSN degrades the network lifetime greatly.