Stiff nonlinear dynamics fails with large step


I am trying to solve contact-implicit optimization using a stiff approximation of ground normal force. From the paper I see

stiff dynamical systems and implicit or differential-algebraic equations, an
implicit integration scheme should often be used

I have tried “LIFTED_IRK” with “SQP_RTI”. The first iteration is very fast compared with ERK. However, it only applies to small steps of 0.01s with 25 steps, during which, I suppose the dynamics has not yet reach the stiff area. Both increase step length and steps N will lead to status 3 (i.e., fail to converge, I think). What should I do?