I'm sorry you had to go through this terrible ordeal. Usually, the banks DO accept the appraised price..Im' not sure what went wrong in your case. Are you sure the listing agent is working closely with the bank? Sometimes, new agents don't want to put in the extra work of going back to the banks to have a price changed, therefore, they don't even try but they tell the buyers, the bank is not accepting it. You should ask for something in writing that the offer was presented to the bank.
Then, if all else fails, think about how much you like this home? What will it mean to lose it? Is it end of the world? Then consider if 10K makes that much of a difference. good luck. :)