The obvious things that come to my mind are your nock point could be too low. Your arrow nocks might not be oriented properly so the cock vane is out to the side and tweaked to give adequate clearance. Your arrows might be too stiff. You might be putting too much heel into the bow's grip occasionally, more likely a big part of the problem if it doesn't do it on every shot. If you're using plastic fletch, it would be a big help to switch to feathers.
If none of those are the problem and you really want to use an elevated rest, then go the 3 Rivers and buy a T-300 flipper. Here's a direct link to the product.
http://www.3riversarchery.com/Product.asp?c=46&s=203&p=0&i=8190X