Thanks for all of the details! I can certainly see the issue now.
One thing that I noticed is that when I create the design, if I select a Linear Constraint, I still have the option for center points. As soon as I select Disallowed Combinations, the center points will disappear. If I switch to linear constraints, it does not appear! Putting the constraints to none, center points reappear, then choose linear constraints and it will stay.
I can see that this behavior has nothing to do with what your constraint is. I am not sure why, so for the best answer you may wish to contact JMP support. I do believe that this behavior is intended though. My best guess is that once you start adding certain combinations that are not possible, determining what is the "center" might be difficult. This is just a guess on my part. Perhaps tech support can provide a better answer.
Dan Obermiller