Just had mine done in our Lincoln MKT and had same issue. Safelite guy came out to fix it and showed me what was wrong. There are two rivets that hold the spring on. They have to be restaked to tighten them up. He did that and mirror is good as new. He advised letting them do it as its very easy to crack the glass when taking it off to fix it.

 

Had my windshield replaced 2 months after I got it in Nov. Mirror still shakes. I read its the spring, didn't take it to the glass guy, didn't have time. But know its really bugging me.

 

Hopefully your instance is the same as mine was. Turns out the mirror actually hadn't been pushed down hard enough. I went to an autoglass shop, described what was going on, and he immediately knew it just hadn't been pressed down hard enough. He said you have to press down so hard you think you're going to crack the windshield. I watched him do it, and he accurately described it lol. Took him about 20 seconds.

 

Thanks for the tip, I'll check it this afternoon.