I guess you could write a book -- a chapter, anyway -- on how players keep the durn things from slipping away. I usually play a Bear Meadow (owner Dwain Wilder drops in here from time to time and may have additional wisdom to shed on the subject) that came with four nicely placed half-discs on the bottom that fit over the thighs and keep it from moving too much. Pioneer dulcimer builder Uncle Ed Thomas did something similar, at least on his earlier models. I have another one that came equipped with a Carpenter Strap (named for player Susan Carpenter, I'm told) that snaps under the thighs and holds it firmly. Atwater-Donnelly, a wonderful duo from R.I., use a loop of string (thick stuff; looks like yarn from a distance). Sally Rogers uses what looks a scarf; I can't say exactly how it's fastened, but it has a lot of visual appeal.
Then there's the matter of the "perfect chair" for playing. That varies from player to player -- height of the legs, angle of the back etc. I found mine in an old wooden office chair (designed for lumbar support, an old label said) at a flea market (oops, I'm taking credit where most of it should go to my wife. She found it; I sat down and said "this is it").