In the present study the reaction-diffusion manifolds (REDIM) method for model reduction is applied to detect extinction strain rates of highly diluted hydrogen/nitrogen and air counter-flow diffusion non-premixed flames at different ambient pressures. The considered problem inhibits miscellaneous challenges for modeling of reactive flows and is therefore well suited for testing the REDIM reduction method. First of all, by assigning critical strain rates the model's ability to capture transient system behavior is investigated. Moreover, critical system regimes of extinction are strongly influenced by the pressure dependence of chain branching and termination mechanisms. This leads to a nonmonotonic dependence between system pressure and extinction limits. The aim of the present work is to find out to what extent the REDIM method is capable to reproduce these complex chemical chain branching and termination channels. Furthermore, in highly diluted hydrogen counter-flow diffusion flames the fast molecular transport of radicals into the reaction zone is strongly affecting the flame stability. Consequently, detailed transport models must be considered in this critical case, which represents an additional task for the reduced model. In the present work, results of reduced simulations based on the REDIM method are compared with detailed calculations and experimental data to show the ability of the REDIM model reduction method to account for such critical regimes of nonstationary combustion processes and to reproduce the nonmonotonic function of critical strain rate dependent on the system pressure in the case of a detailed transport model.