Modern intensive longitudinal data that collect many occasions of data per subject using mobile devices have been increasingly common nowadays. These data collection methods offer important benefits in measuring various traits in the real-life context, such as moods, physical activity and other human behaviors. A common problem occurring in these studies is potentially nonrandom missing data, such as nonresponse to prompts. It is possible that the nonresponse behavior depends on the unobserved values of interest, leading to nonignorable nonresponses. It is important to perform sensitivity analysis to assess the potential impact of nonignorability on standard inference based on ignorable nonresponse. However a sensitivity analysis that directly fits a range of nonignorable models can be challenging to conduct because the resulting likelihood functions from these nonignorable models involve high dimensional integrations, due to the intensiveness feature, missingness in both outcome and covariates as well as non-monotone missingness patterns. In this work, we consider a leading case where both outcome and covariates subject to missingness follow correlated linear mixed effects models and developed index of local sensitivity to nonignorability (ISNIL and ISNIQ) to measure the nonlinear local sensitivity of the missing at random (MAR) estimators to nonignorability for such intensive longitudinal data. This method is tractable to use and completely avoids the need to evaluate those high-dimensional integrals associated with nonignorable nonresponses. We derive the formulas for ISNI index measures and evaluate the performance of the method using simulated data, and apply it to a real dataset obtained using the Ecological Momentary Assessment (EMA) method.