If you move out of the country, the trust will still be valid for assets that are held in the US. If you hold assets outside of the US, it will depend on the country in which you move.
So for example, Canada and Australia recognize the law of trust. England recognizes the law of trust, and most likely your trust would be upheld in those countries. Germany and France do not.
So you will need to consult with someone in the country that you move to, to determine whether you need to do new documents.