Yeah, as eveyone's already said above, it's really hard to find another song like Duty. But if you haven't really listened to her earlier albums, I think you'll find more songs that are similar to it in those albums than say, Secret. :/
LOVEppears isn't really anything like Duty...hm...I might suggest just going through the Duty, I am..., and RAINBOW albums (not so much RAINBOW, but there's a little bit of her Duty era still in there) just to see what you might find.
BTW, Duty's one of my favorite songs, too.
I tend to always listen to Duty and then follow it up with Heartplace and/or Over from RAINBOW and Scar (I*think* from A song for XX) and End of the World (not sure which album it's from...:/). I always associate certain songs with others of the same sort, so maybe you might like those songs too.
Good luck, though! You have good tastes!
Oh, also!! I think that (now that I think about it) Hanabi might be the closest song that I can think of. It's also on my list of things to place with Duty everytime
Can't believe I forgot that. XD