If you find a collector in your studio who wants a discount on a painting, ask them if it is because they can't afford the work or because they don't think it is worth the price.
The real answer to the question is it gives them a sense of empowerment, and they become superior in some way by being the better business person. Unfortunately it makes the artist feel discounted, not just the artwork.
When a collector buys artwork, they are in many ways giving the artist a belief in himself and a stamp of approval. With the discount thing, it reduces any transaction to strickly business. It may save the buyer a few dollars which may be part of the prize but know that it says to the artist, "we think less of you."
This of course applies to work that is fairly priced to begin with and that is always subjective but I think most people will know what is fair and what is outrageous.