Awesome recommendations. I fixed my floppy visor.
Before & after fixed:

Before

The separated support

Glued and cleaned in place.

No more flop.

 

I went the screw route on this thinking it would be stronger. I used 4 flathead #5 screws. Overall length .700" I drilled a .122" diameter clearance hole and a small .060" hole in the mating side for the screw to tap into. This is a satisfying fix and cost the price of some flathead screws. Countersinking the very top of the plastic will help the screw fit flush. Also, when you drill through the plastic don't apply much pressure. Let the drill do the work and drill slowly-you don't want to drill thru the leather (or suede) on the other side. Set the drill on the slowest setting possible. The overall length of the screw you use is critical. Too short and it wont have enough plastic to thread into. Too long and you could feel the end of the screw behind the material when your finished.

 

Modified Truss Head screws may have been a better choice as they don't protrude up or down, but pretty much totally flat. The flat underside would transfer less lateral forces to the plastic also, by not forcing a cone into the hole.