The 9th U.S. Circuit Court of Appeals in San Francisco ruled that the public has no right to see the footage on Thursday.
The 2010 trial was the first in a federal court to examine if prohibiting gay couples from marrying violates their constitutional rights.
Gay rights advocates said they wanted to use the recordings to try to puncture political arguments used by opponents of same-sex marriage. However the U.S. Supreme Court forbade the footage from being made public after the ban's sponsors argued that distributing trial footage could subject their witnesses to harassment.
The trial was open to the public and received widespread media coverage, so the recordings would not have revealed any new evidence or testimony.
However, the appeals court must still rule on whether the decision to strike /*Proposition 8*/ down abided by federal constitutional grounds. Arguments have been heard on that issue a year ago, but the court does not face a deadline for making a decision.
The Associated Press contributed to this story.
