Yes, they do. I think the only problem with elites is that you only get the quest bonus if you defeat the monster AFTER you got the quest. So if you already killed it, you'd have to do it again, but that's usually not such a big deal.
I'm pretty sure you can't "miss" monsters/quest. If you can kill a Unique before taking a quest involving it, then it will always respawn (even if you have trouble to find it again) And the monsters you can't find anymore are from certain quest you already beatten. (but not all of them).
It can be confusing because some monsters appears near others, you can easily think you killed one instead of another (except if you remember all the Unique's name).
The only way to miss a monster is to pass any point in the game where the quest is not available anymore for X reason I think. --- Currently waiting for... Earth Seeker. We'll see.
That's what I was thinking too, but the possibility is low. I was hoping to say the truth for the game's sake T-T I checked on the japanese @wiki guide and it seems that way, but I may have been translating too fast... --- Currently waiting for... Earth Seeker. We'll see.