The reasons why a U.S. consulate will deny someone a visitor visa depends in part on which country they are from. It does not help that you are a U.S. citizen as they will assume that your parents have the intent to live in the U.S. permanently. Since the visitor visa was denied more than once, it is not very likely that it will ever be issued. You do have the option of applying for green cards on their behalf and if at some point in the future, they wish to abandon that status, they can do so. So long as you remain a U.S. citizen, you can always refile for green cards for them at some point in the future.
Answered on Mar 15th, 2013 at 10:34 AM