Yes you can based on what is stated above. It sounds like what they have is a pre qualification letter and not a commitment letter. Generally in a contract the commitment date is set to be approved for the loan. Ideally by this date all conditions have been met in order to get the loan. It sounds like they are just starting the process over again.
Remember, it could have been the lender that was holding things up before, and the buyer is really doing their best to get things done. If they are going to pay for a 2nd appraisal I am assuming they are putting forth effort, so you should take that into consideration. I've come across lenders who just didn't have their act together and it was necessary for a buyer to go somewhere else. You don't want to throw out a good opportunity to move on with things. What is your agent suggesting?