It's difficult to say what might have gone wrong. One important modifier is the player's race and class. For instance, Sera is very easy to romance as a qunari warrior or rogue, and very difficult to romance as an elven mage (and impossible to romance as a man). If you happen to be an elven mage, you have to squeeze all the approval out of her that you can find, which can be quite challenging.
From what you described, the romance quest should have started, but just in case you still haven't maxed approval, try to find some Red Jenny caches if you haven't already.
