I dont know about this car specifically, but an old car I had did this and I was able to stiffen it up with some stick on foam between the part that moved the slats and the side of the vent. Have you taken it apart to look at it?
Is this the vent? If so looks like you can take it apart with some torx screws and see whats going on. Or you can just replace it. It looks to be just held in with clips.
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