Greg,
As others stated, read your purchase contract so you know what your rights are and where you stand.
Secondly, the advice of find another buyer and not waste your time may not be the best advice. While it is a common emotional reaction to a buyer like this, you must consider the costs of starting over again.
First and foremost, if you have the right via contract to reduce down to appraisal price, then you simple inform your buyer they have no more contingencies to back out and you will sue them for damages for not closing.
If you don't have that option, you will want to stay on the nice side and explain to them what I mentioned before regarding appraisals, that you will come down to that price, and that the costs for them (appraisal, inspection fees,time, etc) to move to another potential purchase may waste all the savings they think they are missing. Then, if all that does not work, you have to consier what the costs are for you to start over, how difficult it is in your market to find a buyer for this property, and weigh that against giving this buyer something else in addition to the $2k reduction.