Studying on networked systems, in which a communication between nodes is functional if their distance under a given metric is lower than a pre-defined threshold, has received significant attention recently. In this work, we propose a metric to measure network resilience on guaranteeing the pre-defined performance constraint. This metric is investigated under an optimization problem, namely \textbf{Length-bounded Paths Interdiction in Continuous Domain} (cLPI), which aims to identify a minimum set of nodes whose changes cause routing paths between nodes become undesirable for the network service. We show the problem is NP-hard and propose a framework by designing two oracles, \textit{Threshold Blocking} (TB) and \textit{Critical Path Listing} (CPL), which communicate back and forth to construct a feasible solution to cLPI with theoretical bicriteria approximation guarantees. Based on this framework, we propose two solutions for each oracle. Each combination of one solution to \tb and one solution to \cpl gives us a solution to cLPI. The bicriteria guarantee of our algorithms allows us to control the solutions's trade-off between the returned size and the performance accuracy. New insights into the advantages of each solution are further discussed via experimental analysis.