There seems to be a maximum amount of approval for companions. Just stopped getting Cassandra approval myself last night (though I am playing a female, so no romance).
Here is what I found on the web after quick searching:
http://gaming.stackexchange.com/questions/193471/is-it-possible-to-max-a-companions-approval-rating
As for the romance, she will just keep giving you that line about spending more time together until you activate the romance. For me that was after "The Verchiel March", and I spoke to her again and she sat me down in her Skyhold quarters and had a heart to heart about starting the romance (had to clear things up with Josie first). I know from some guides that there are some story decisions that can close off romance possiblilities, so its possible you triggered one of those (something surrounding Mythal but I haven't gotten that far so I don't have details). It is mentioned in the IGN guide. Also note for the Sera romance, being an Elf female is the most difficult (she has a preference, being Qunari>Human/Dwarf>Elf).
I have read that if you wait too long in the story the characters aren't romancable (become locked out) but I'm not sure about that. However, I have held back from story missions forever (still waiting to do Wicked hearts after 100 hours). You will probably have to dig around on the interent and Bioware boards (there is a Sera specific thread), but It sounds like you may have triggered a romance lock out and you are now capped for approval level so that romance can not be triggered (especially if the heart option vanished). Hopefully you've been keeping some hard save points and can go back.
Thanks a lot for the answer. Yes, thankfully I've learned from experience that it´s good to keep some saves, so has a lot of them. Just don´t feel like going back so long right now though so will probably just start a new character and deal with that later. Think it might have gotten stuck on "let´s travel around some more" somehow. In future games I will always worry when a character says that thanks to this ☹️ Think it would be better if it would just trigger automatically if you have maxed out approval and choose that dialogue option. So guess I´ll get back to that character when it is fixed or when there is some kind of cheat to trigger the romance :P
