Perhaps it's not about death. It may be about some sort of separation within the Shard. After all, both Ruin and Preservation have their bodies/power manifest themselves in the mortal world. And the Allmighty kind of has... everything separated from him. We don't know enough about Endowment to back up that claim, but it could be that the divine breath is a part of him.
We have that.
We know that Divine Breaths are Splinters,
And we know that splinters are a piece of a shard that is non-human,
and we know that Endowment is the Voice that speaks to the Returned, offering to let them return.
And we know that the Divine Breath allows them to Return.
So, it makes sense that Divine Breaths come from Endowment.
1. Both gods could, if they wanted, fuel all of the metallic arts. Preservation is stronger at fueling Allomancy, Ruin stronger at fueling Allomancy or Feruchemy when it has been given via a spike. Both are balanced when it comes to Feruchemy. But this rarely comes up in the books, as it required expending power in a way that the gods were hesitant to do.
Now, personally, I think that Divine Breath is Endowment doling out his power in a way that Ruin and Endowment are "hesitant to do".