How do I repair plantation shutters
I used to own and run a Blind business.  Living in Florida, a majority of our volume were shutters.  I would suggest getting a staple that is slightly longer than the one that came out  and then pushing the new one in.

I would protect the lever with a towel and then use a wide wrench, like a plumbers wrench, to squeeze the staple in.  Another option which would probably be easier would be to use the same size staple that fell out and use a two-part epoxy to set them in the holes.  You may have to get a small syringe to inject the mix into the tiny holes before inserting the staple.