Scott,
The reason the screw is loosening on the left side and not the right is the direction of the wheels. The right-side drivers turn clockwise going forward and the left turns counter clockwise. And we all know that most screws are right hand threads which are loosed by turning counter clockwise.
Laptop screws have Loctite preapplied and they always come apart.
I would apply a small amount of purple Loctite and let it dry on the screw and then install it. This way it’s not really bonding the 2 threads together.
BTW, if you ever run into an instance where the wrong type of Loctite is used and you need to take something apart, use a pencil type soldering iron and heat the screw head.