Check out the information at the link below. Altering the singularity elimination factor should only occur if all other options have been exhausted. Lowering this factor assists in reducing stiffness singularities created from large displacements or high strains. A Nonlinear study is able to recalculate the stiffness matrix of the part at every step, and the singularity elimination factor is applied into these stiffness matricies if stiffness singularites appear...
Can you show us how your stress-strain curve looks?
The message you mention can have multiple causes, but usually it is due to buckling or divergence in an element.