Well, thank you for telling me. How would an asexual romance work, then?
Honestly, that's the thing I keep coming back to. Thinking about it in the Dragon Age world, it would be hard to depict a character like this, because do Thedosians understand the differences between sexual and emotional attraction? Perhaps a member of the Qun would, and maybe that could be something to look into.
(A qunari Tal-Vashoth who left the Qun and tried sex a few times because it wasn't allowed, but not because she felt the urge to. Realized it just wasn't for her, and carried on. Prefers having her hair brushed to kissing.)
One way to do it could be an ace LI who isn't repulsed by sexual contact, that way even sexual characters don't feel like a zot has been 'wasted' on an asexual LI. The ace LI has to be asked about sex, and maybe he turns you down the first time, because he's just not up for it. You ask again, later, and he says he hadn't thought about it, but he's willing. The scene after would be really hard, though, because how do you depict someone who's happy the Player is happy, but really just wants to get back to trimming the feathers on his arrows? And not insult the Player?
On that same note, how do you make sure that it's actually asexual representation there? You can't say the word 'asexual', that term doesn't exist in Thedas. But you also can't say, "I don't want to have sex with you," because most players will take that as a rejection. You could have the ace LI explain further, but how do you do that without coming across as an Asexuality 101 professor? There's a fine line that has to be balanced there. But... I think it could be done.
I feel there would have to be 5 things for an asexual relationship in Dragon Age:
1) Obvious Asexual Representation - If you're going to do it, make sure the character reads as asexual. Otherwise, what's the point? The character has to be disinterested in sex, and the only way I can think to show that is to, simply, not have them come to the Player asking for sex. 
2) Content for Sexual Players - The asexual crowd is itty-bitty, and the sexual one has shown they generally don't like their LI's to be chaste. (Sebastian.) So, write the asexual LI that's willing to have sex, but you have to make sure the character is still asexual. Asexual people can have sex, can enjoy sex, but really we'd rather be doing something more productive. Perhaps the after-sex scene could be a sexual Player waking up and seeing the asexual LI, freshly-washed, doing some work in a chair.
3) Content for Asexual Players - If you're not gonna have sex, what are you going to be doing? Talking about all that sex you're not having? I hope not. There does need to be a conversation, though, or else it's not representation, it's ambiguous. So, perhaps something like, "So, you ever gonna ask me to have sex?" "Uh, no. Why? Do you wanna have sex?" "Nnnnnooo... It's just... everyone else always asks me to have sex." "Ugh. Why? Let's play chess." and that's it. Then we get lovely scenes with cuddling and hugging and nuzzling and face-touching. All the face-touching.
4) Ability to Be Asexual as a Player - Let me say, as plainly as I can in the game world, that my character is asexual. And don't make the Player automatically act approving to a flirt. The Reaction Wheel sounds like it could be perfect for this kind of thing.
5) Team Banter About an Asexual Relationship - This is probably where the character will talk most about their asexuality, actually. And, really, part of this banter would end up, for an asexual pair, being about all the sex they're not having. And that's great. No, really, this is important here. Acknowledging that these two characters are not having sex is important. Acknowledgement from the outside world is important.
Aaaand, that's all I can think of. I should preface this by saying I in no way speak for all asexuals. This is just what I would be comfortable seeing in a game, and what I hope for in an asexual relationship. Really, at the end of the day, all I want is acknowledgement and love. Just have to make that work in this kind of setting. 