How do you keep a knit beret from falling off?

You use a clip to keep it in place.

When women wore hats all the time they used hat pins. You can still find them at antique and thrift stores. There is a huge variety of hat pins to match any hat or style, and they really do work to keep your hat on your head. They're basically a longer straight pin with a duller head and some form of decoration. You poke it through the hat, slide it under some hair and poke it back out of the hat. You can place them wherever you need them to secure your hat on your head.