The best harmonica rack I've seen has 3 tightening screws instead of the usual 2. The harmonica is held in these two wire thingies which grip it from either end. Sorry, I do not recall the make. It's not as easy changing them with this one, but it works better for holding the harp and not sinking to half-mast while you're playing.
Another thing you can do is put small lock-washers under the screws to increase their grip when tightened.