Two important notes:

  1. You need to call layoutIfNeeded within the animation block. Apple actually recommends you call it once before the animation block to ensure that all pending layout operations have been completed

  2. You need to call it specifically on the parent view (e.g. self.view), not the child view that has the constraints attached to it. Doing so will update all constrained views, including animating other views that might be constrained to the view that you changed the constraint of (e.g. View B is attached to the bottom of View A and you just changed View A's top offset and you want View B to animate with it)

Try this:

Objective-C

- (void)moveBannerOffScreen {
    [self.view layoutIfNeeded];

    [UIView animateWithDuration:5
        animations:^{
            self._addBannerDistanceFromBottomConstraint.constant = -32;
            [self.view layoutIfNeeded]; // Called on parent view
        }];
    bannerIsVisible = FALSE;
}

- (void)moveBannerOnScreen { 
    [self.view layoutIfNeeded];

    [UIView animateWithDuration:5
        animations:^{
            self._addBannerDistanceFromBottomConstraint.constant = 0;
            [self.view layoutIfNeeded]; // Called on parent view
        }];
    bannerIsVisible = TRUE;
}

Swift 3

UIView.animate(withDuration: 5) {
    self._addBannerDistanceFromBottomConstraint.constant = 0
    self.view.layoutIfNeeded()
}