Are you sure it is the joint and not where the bracket attaches to the windshield? There is an allen type set screw that attaches the mirror to the metal base that is glued to the windshield. That is a common loose mirror issue and can be fixed by tightening the screw, but if it is in one of the joints you just need a new mirror.
My 06 rear view mirror is also a bit loose at the pivot joint, not at the base-windshield. I will try some rosin powder on the joint ball to increase the friction, like applying rosin powder on violin bow.