DeathTime not working correctly in combination with /scoreboard

I hooked up a commandblock to a redstone-block clock, giving it 20 pulses each second, and inserted the following command:
[CODE]/scoreboard players set @e[type=Zombie] Die 1 {DeathTime:0s}/CODE
with Die being made as .
[code]/scoreboard objectives add Die dummy Die/code
I put a commandblock before it that would trigger earlier in the tick, with the following code:
[code]/scoreboard players set @e[type=Zombie] Die 0/code
This should set all the scores of the zombies that are dead (becoming corpse) to 0, and all others to one. For some reason the zombies die, but the score stays 1 forever.