Preview signs only update their contents when you try to move an item or look in the chest again. I suggest the preview signs update every few seconds, or whenever the chest updates. Dunno how much server lag this would cause though.
It used to only update when you re-opened. I think the addition of when you click on it, is really good enough. Not everyone will agree; but there just doesn't seem to be a compelling reason why it should be changing that often