There are both an outer and an inner iteration. The outer one is executed in all cases where you have a non-linear equation system to solve (unconfined aquifers, unsaturated simulation, density-dependent simulation, ...). The inner one is the solver iteration, and this one you do not have in case of a direct equation-system solver. The non-convergence message refers to the outer iteration that is controlled by the error criterion on the Numerical Parameters page of the Problem Settings dialog.