Can a bank refuse to accept a appraisal they ordered?

Yes. The appraiser is a 3rd party and is independent of the bank. They are not forced to lend on a bad report. If you paid for it, you can ask for your money back but they are making a financial decision to which they are held accountable for up to 30 years and appraisers are not perfect. All appraisals do go through a review process. Not doing so would be a bad decision by the bank.

It is rare but it can happen for reasons Mario has stated. Have you been told specifically what the issue with it is? I am a mortgage lender with 30+ years experience in Albuquerque and would be glad to review the report if you have a copy of it. Feel free to contact me. charlie.sparks@financeofamerica.com or 505-350-3745 (cell/text). NMLS# 195031

Yes... very rare, but it can happen. I just had one rejected. Appraisals have to be randomly assigned. We got one back recently, and it was assigned to an appraiser on our naughty list of bad appraisers, and was therefore rejected.