If a model fails to converge, it could be because the default solver settings are too aggressive. There is always a tradeoff between speed and robustness, and the default settings cannot satisfy all cases. The key solver setting that can be changed to help with convergence can be found in the Fully Coupled node under Stationary Solver in the Time Periodic study. In the Method and Termination section, there is a parameter called Restriction for step-size increase (default value 0.05). This controls how much the damping factor can change between subsequent iterations. If it is difficult to obtain convergence (for a model whose chemistry has been validated in 1D, and is adequately meshed), it is worth lowering the value to 0.02, or even 0.01. This means the solver will have to take more iterations to solve, but it should be more stable.