The mirror post has a tension spring held on by what some call a "Palnut". It is not really a nut, but a thin spring steel washer with fingers that stick inward. When pressed on, the fingers grip the stud, and the spring tension pushes back against it keeping it in place. Most likely culprit is the washer cracked between two fingers, releasing it's grip.

The washer would nut be a serviceable part by itself. It may be possible to find one non OEM. I have a mirror off that has a damaged base. When you get yours off, send me a picture so I can see what is up with it.