Longitudinal non-Gaussian data subject to potentially non-ignorable dropout is a challenging problem. Frequently an analysis has to rely on some strong but unverifiable assumptions, among which ignorability is a key one. Sensitivity analysis has been advocated to assess the likely effect of alternative assumptions about dropout mechanism on such an analysis. Previously, Ma et al. applied a general index of local sensitivity to non-ignorability (ISNI) to measure the sensitivity of missing at random (MAR) estimates to small departures from ignorability for multivariate normal outcomes. In this paper, we extend the ISNI methodology to handle longitudinal non-Gaussian data subject to non-ignorable dropout. Specifically, we propose to quantify the sensitivity of inferences in the neighborhood of an MAR generalized linear mixed model for longitudinal data. Through a simulation study, we evaluate the performance of the proposed methodology. We then illustrate the methodology in one real example: smoking-cessation data.