I had a quick look on the simulation (haven’t tried to run it myself), but I think this error might be due to the elastic support that stabilizes the inner body not being stiff enough, so try augmenting the value.
Other aspects I would consider for this simulation:
You will need a plasticity model for the material that is being stamped.
Move the die closer to reduce simulation time, just shy of the start of contact.
Did you check the formula for the movement for the die? The speed and amplitude are important for the simulation, if it is too fast it might be hard to achieve convergence, if it is too slow you might be wasting simulation time.
I think you don’t need the X plane restriction, at least for the dies. On the material I would try with and without and see the difference.