They don't bring back the dead, they bring what you thought of them to life.
You must agree with me that, unless we bring things such as souls and the afterlife, bringing an animal back to life (in the sense that every single cell in its body has already died and suddenly being reanimated) is impossible. Yet life points seem incredibly persistent into doing its best to comfort you by granting your wish of bringing someone back to life.
So what are they doing? Reading your mind, of course. Life points will probe the brain of the wishers for any information regarding what they're trying to bring back to life, such as species, overall behavior, mannerisms, habits, etc. Once it's complete, it will go haywire, absorbing as much components as possible to achieve the necessary mass. Once it's gotten what it needed, a life point will enter a pupa stage, creating a flexible cocoon around it and undergoing a metamorphosis stage, in which it will acquire the appearance and traits of the dead person/animal, doing its best to replicate as well as possible.
Once the pupa stage is over, your precious loved one, pet, friend or whatever being you wished for will return...kinda. Are you sure your friend who was so nice to you was nice to everyone? Or that your grandmother treated her friends exactly like you? A life point can't really bring the person to life, and in its attempt to grant your wish, it will replicate not the deceased person or animal, but your idealized version of them based on your own experience. That is why the ones brought back seem off to those other than you and don't seem to have many memories. How could the life point fully remember a party your grandpa went to if all you know about it comes from pictures and from your grandfather's stories.
Life points aren't perfect, they're biological organisms with incredible abilities, yes, but they aren't omniscient. It can't give back what was lost by the natural life cycle, but maybe it can make a desolate wishers happy by giving them an illusion that might just be good enough.