AFAIK the only way to do it is to delete one of the hinged objects.
Delete one of the hinged objects, then recreate it again in the same x.y location and angle, then re-hinge it.
This is the method I used in Tonks for recreating the tank treads should they "fall off" the tank. That was a bug at the time which is now fixed, but it was the only way to make it work at the time.
I stored the objects X, Y, and angle values in private variables, so as the object was deleted it was recreated instantly. You never knew it was gone.