Fading

Fading is the only way that gods and monsters can truly die. It is caused at least partially by diminishing of their realm or people not believing in their principles. Gods that are not well remembered or were never worshiped can also fade. Gods seem to be able to resist fading on some level or the demigods supply enough belief to keep them from fading. It appears that belief in oneself and a loss of the will to live can have great influence on fading; it is unknown if a god must consciously give in to the process in order to fade or if it will inevitably overtake them.

Gaea was shown to be able to revive at least Stheno and Euryale, hinting it can be reversed.

The Battle of the Labyrinth
Demigod children of Hades can detect the fading of gods, or perhaps just when a dead or semi-dead god is near, as seen in The Battle of the Labyrinth by Nico di Angelo when he reveals that Pan is indeed fading, that what they see is more like a memory that can't pass on.

Pan is only god that Percy sees fading during the entire series. His fading was caused by the rapid diminishing of his realm, as there are almost no wild places left on earth. He was able to resist completely passing away for many centuries, but it is unknown if he could have done so indefinitely. Just before he faded, he passed his power on to Grover and friends, giving the implication that fading gods can entrust a portion or all of their powers to a mortal or demigod (unknown if they could pass it to a god).

The Lost Hero
In The Lost Hero, while Leo Valdez is fighting Khione, she turns into snow and he destroys the snow by setting his hammers on fire and throwing them at it. However, just before this, Khione tells them not to think they've won anything, because Gaea would wake before they could ever stop her. This indicates that she is still alive, although it is also possible that she faded.

The Son of Neptune
Stheno and Euryale, Medusa's sisters who faded, were revived by Gaea and attacked Percy Jackson. It is unknown how this happened.

Known Faders

 * Medusa´s Gorgon sisters, Stheno and Euryale (Some how Revived by Gaea)
 * Titans Helios and Selene and Eos
 * The Cyclops that accompanied Polyphemus
 * Hekatonkheire, Cottus and Gyges
 * Pan
 * Ouranos