Refunding of the fee is up to the individual bank and their management. You can take your request to a higher level of management and see if you get a different answer.
Appraisals are performed, and due, regardless of whether the value meets the sales price, the condition of the home is perfect, or the loan closes. IF you had taken the first contract to fruition and been denied due to income circumstances (and you’d fully disclosed all details of your employment to your loan officer), you MIGHT be justified in asking for appraisal money back. In your case, however, the appraisal you paid for was completed, and the contract cancelled due to low value. Not the appraiser’s fault the value wasn’t there, in fact, a low appraisal usually ends up protecting the buyer from overpaying. Have to say since services were rendered, there is no recourse for a refund.