To encode information reliably, first spike latency should be sensitive to sensory inputs but robust to external perturbations. This paper studies the robustness of the first spike latency in spiking neuron models. These models are nonlinear and possibly high-dimensional. Understanding which parameters govern the first spike latency sensitivity in these systems generally requires extensive numerical simulations. We show that a local sensitivity analysis of the system is a good predictor of the global robustness of the latency code. This analysis, motivated by previous work on delayed decision-making in bistable models [3], relies on the assumption that the model posses a saddle node bifurcation with a sufficiently attractive center manifold. Results are illustrated on a 6-dimensional model including a K⁺-current of type A [4], a current of particular importance for first spike latencies, see Figure 1.