I've played more and increased Abbie's rating repeatedly. unlike Lola's relationship, Abbie's doesn't show in the book in the room. I keep doing the same dailies and nothing changes. How in the world am I supposed to get it to advance?
If it's not showing at all, that means you've not triggered it to start yet. I guess you skipped first break on day 1 as that's the only way I know of to get through the first day without it starting. What you need to do is talk to Abbie in the yard during first break on any school day and that should give you the quest.