Eve dies if Mordin did not have access to Maelon's data from the Mass Effect 2 mission Old Blood.
There are two ways that he wouldn't have access: If you completed the mission in ME2, but chose to destroy the data, or if you never completed the mission in ME2. The latter of these is the default assumption in a New Game without an imported save.
Without Maelon's data, Mordin is unable to effectively counteract the immunodeficiency that is a side effect of the experimental Genophage cure to which Eve was exposed. Since Mordin is unable to treat her, Eve doesn't make it.
The only way to keep Eve alive is to complete Old Blood on an imported character, and save the data.
Eves survival has two major effects:
- If Eve dies, there is a -50 modifier on Krogan War Assets. Her survival prevents this.
- If Eve survives, you are unable to convince Mordin to sabotage the cure - the only way to do so is to kill Mordin yourself. You monster.