If I were you I would scare it stiff!
And if that doesn't work try driving on smoother roads.
And if you can't make that happen, take an adjustable end wrench and find the chrome part that attaches to the door where the mirror is. The "nut" looks more like a decoration, but using an adjustable end wrench you can tighten where the mirror mounts to the car.
If that doesn't work see if you can mount your girlfriend or wife. Sometimes all you've got to do is ask! It's worth a try!