Of course, the buyer is also free to not to buy it.
But as an instruction to a consignment shop, “reasonable” means he may not be wasting his time by calling you when a prospective buyer makes an offer below asking price.
If you are authorizing the seller to approve a discount without consulting you, you really must dictate a maximum discount in your consignment agreement.
As to what discount is fair, others have already described a few of the two or three thousand things that might go into that decision.
Maybe there are useful parallels in this story: I have offered one of my fine German tubas for sale, but the offers I have received have been constrained by the new (and, it must be said, quite playable) Chinese instruments on the market. My price is reasonable and I am not desperate. So, unsold it remains, and will remain until my heirs have to deal with it. It’s a matter of respect for the instrument, it’s maker and it’s history and provenance (and it’s playing quality). But if I was desperate, or any of many other factors were true, I might let it go at a lower price. Again, it’s a matter of respect for the instrument. But it’s also based on a real understanding of comparable instruments and inherent value. Most (not all) other experts I have consulted have validated my assessment, but only after inspecting and playing the instrument themselves.
—Rick