In wireless sensor networks (WSNs), the data observed by different nodes must be relayed safely to the base station over intermediate nodes. In the network environment, some sensor nodes can act suspiciously when they enter someone else's control or due to other equipment failure. Data packets that are sent through suspicious nodes may be randomly dropped or may be not delivered as desired. In this paper, we investigate the impact of disabling suspicious nodes communications on network lifetime through a linear programming framework. We build a mathematical programming framework and perform comprehensive numerical analysis. Our results show that the decrease in WSN lifetime is less than 8.0% if the number of suspicious nodes is not higher than 10%.