Hello, I am answering from what I understood using the rules in player core.
First of all, Curse of Death duration is "Sustained up to 1 minute"
The entry for Curse of Death states "This curse ends when the spell ends"
So basically sustaining the spell, prevents the curse from falling off the target. Now to the second part.
A Curse is an Affliction, and it has a initial saving throw, and subsequent saving throws. The success on the initial saving throw prevents it from going into further stages, but as it is an affliction, every time the time in parenthesis goes by, a subsequent saving throw has to be made. For this case it is 1 round.
In this spot the 4 degrees of success will have the following effects:
Critical Success: Reduce affliction by 2 stages
Success: Reduce affliction by 1 stage
Failure: Increase affliction by 1 stage
Critical Failure: Increase affliction by 2 stages
So depending on the result you move the affliction the number of stages and apply the described effect for it's current stage. In this particular case, Success and Critical Success should move the affliction to stage 0, and hence dropping the affliction (no need to sustain anymore) or they can fail, and the stage will not increase, since they succeeded the initial saving throw, and can't go past stage 1, they enter stage 1, and get the stage 1 damage applied again.
So why do you have to sustain the Curse of Death, if you don't sustain the spell, the curse drops.
What remains uncertain to me, is if the fatigued falls off if the curse falls of. Thinking about it as part of the affliction, it should, but looking at the Fatigue effect, it should linger until they take a full rest.
