I'm neither an expert nor an official source for rulings, but I would say that the demon continues to be bound and acts as you wish. I base this opinion on the fact that summoned demons act as if under a Bind Demon spell and according to the official FAQ, the death of the caster doesn't end the Bind Demon spell. If death doesn't end the spell, I wouldn't think moving off board would. I may be wrong, but that is the way I would play it. Hopefully Joe will come along and let us know the official ruling.
William