No.  Your question arises from statutory thinking, so if our trust were statutory, you might be correct - - that changing domicile might cause complications that would require re-doing the paperwork.  But in the case of our Natural Law Trusts, the fact that they are non-statutory makes them non-attached to any particular jurisdiction.  That frees its officers to move, travel, and operate anywhere in the world, without any changes needed to the trust at all.  That is why we call them “international”.  The only thing that might change is where one’s bank account for the trust is.