Quaid turned up for a hearing at the Immigration and Refugee Board in Vancouver on Tuesday to state his case for sanctuary.
But the actor's hearing was delayed after his lawyer asked for more time to review documents, reports Eonline.com.
It's the second time this month that attorney Catherine Sas requested and received a continuance to allow further preparation.
A new refugee hearing has not been scheduled but a pre-hearing is set for December 22.
Quaid and his wife Evi were arrested in Vancouver last month on outstanding U.S. warrants related to vandalism charges.
They are wanted in Santa Barbara, California, where they missed a third court hearing in as many weeks earlier this month.
The couple fled to Canada after alleging they were being persecuted by "Hollywood star whackers" and that their lives were in danger.