From a gameplay perspective, I can imagine that it's not nice to have active aura's on dying creatures. Many monsters have a lot of hitpoints, and even a coup-de-grace or two won't necessarily take them out. It may turn into a jarring stomp-on-the-dead scene, which I'd like to avoid.
From a consistency standpoint; well, when does and aura stop? Why would an intense fire aura suddenly stop at 0 hitpoints - but why instantly stop when the creature is dead? That kind of thing is just really flavor specific. But regeneration also stops when creatures hit 0 hitpoints: Basically, to me, it suggests that at 0 hitpoints, creatures are as good as dead - they've a chance to recover still - but they're out of it at the moment. Aura's can be suppressed and restarted as a minor action, in general - which suggests that there's is some level of conscious control (in some vague general sense).
So, for gameplay reasons primarily, and to reflect the fact that there is normally some amount of conscious focus involved, and to mirror the fact that pretty much everything else you do stops at 0 hit points, I'd say aura's cease when a creature drops, except in specific situations where believability or drama demand otherwise.