The problem: the little plastic tabs holding the helmet visor in place broke! When I rode, the visor always flipped up and back. Tape is sloppy. Glue can affect the integrity of the helmet by dissolving the plastic and foam. Simply ripping the visor off is workable, but the helmet looks even dumber than before.
The solution: Hook and loop fasteners! These happen to be Velcro brand, but any hook-and-loop fasteners with adhesive backing should work. I bought this package from Home Depot, but I'm sure any hardware/home improvement store will carry this stuff.
Cut to size and attach hook and loop fasteners -- stick one piece on the helmet, and attach the other piece to the visor, ensuring the two pieces line up.
All happy! Your visor will now stay in place. My job is a little sloppy; I'm sure you can do better.