Barb--
Most likely the splines (those little lengthwise ridges or teeth) around the inside of the on/off switch knob are stripped; I presume the knob is plastic. A new knob would be the solution, and you may be able to find a generic replacement knob at a hardware or electrical appliance repair store.
Chip
March 2006
I can answer this question...
HOW DO I FIX A SLIPPING ON AND OFF KNOB ON A PORTABLE FAN?
howtomendit.com for free repair help, information and advice.
Try fixfault.com to fix electric fans.