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Is the contact between the punch and sheet frictionless? That would explain why the center of the sheet goes down further than you expect. The reason is the wedge angle between the punch and the die since the punch has a radius and the die has a flat plane. The angle between the punch and die at the end of the sheet causes a tangential force on each end of the sheet to push it toward the center.
One way to fix that is to make the punch have the same two flats at the same angle as the die, except put a blend at the tip of the punch where there is a gap in the die. Another way to fix that is to add friction to the simulation, but that may not be as reliable as the first method.