I'd rather just go kill 3 people, then lose that 1 point for not finding health, than kill 1 person than look around for 10 minutes just to get killed looking for a health pack.
I wouldn't drain rapidly.
It would be more like..
"Ok, just killed three people. And i'm at around 15 health left. Time to go looking for health packs"
It wouldn't be like..
"forget stuff forget, I NEED A HEALTH PACK OR EL- stuff forget I DIED"
I figure it should drain 1 health every 3 seconds.