I've been meaning to bring this up for you guys for a while. I actually found a fic where with an asexual main character. It's an SAO fic known as the
Nightblade series. The main character is an exceptionally well-written OC and the author himself is asexual. I should mention off the bat that the story gets really dark as the OC ends up killing
a lot of people. The OC doesn't get into a relationship until the second "book" when someone comes to comfort him when he is at his lowest, but damn if it isn't beautiful.
EDIT:
Correction: The OC, Rythin, gets into a relationship at the end of chapter 11 of Nightblade I, but the relationship starts at the beginning of the following chapter. Nightblade II is when the relationship reaches its "second stage" of trust, the stage where Rythin confides in his loved one for a second time for a different reason. I should reiterate that the relationship takes a while to actually happen.
What makes the relatiionship so special is that Rythin seems to hate just about everything, including physical contact. It seems to freak him out a little. In chapter 11, Rythin is hurting so much that he becomes
desperate for comfort and the warmth of another human being.
I really do need to applaud the author for making an OC with so much depth.