You probably aren't configuring your GTLServiceDrive with the GTMOAuth2Authentication instance you get after successful authentication.

Example code:

- (void)viewController:(GTMOAuth2ViewControllerTouch *)viewController finishedWithAuth:(GTMOAuth2Authentication *)authResult error:(NSError *)error
{
    if (error) {
        // Auth failed, handle the error
    }
    else {
        self.driveService.authorizer = authResult;
    }
}