I use the 350 almost daily and I have experience the same thing on a number of occasions. The tendency for this flip out to do this comes from over extending it's flipped out position. I, too, have found that "re-alligning" the plastic 'clip' at the base allows for the screen to operate properly again. It is fragile, simple as that.
Be careful when operating these cameras with the flip out monitor open. I would suggest to only use the monitor in the flipped out position, with exceptions of course, when the camera is mounted to a tripod. Using it in the flipped out position when hand held is when the chances for overextending it are greater.