In some Fire Emblem worlds, permadeath really is, well, permanent. Trying to bring back the dead has ghastly consquences in Magvel. Ninian's resurrection in Elibe is both exceptional and more than a little... sketchy.
Not so in Archanea. Though the Aum staff is long-lost and legendary by the time of the War of Darkness (FE1/11), the fact that the thing is housed in a temple known as the Resurrectory suggests that, at some point, it was both well-known and functional. (Worth noting here that, IIRC, the staff could only be used in said temple in FE1. Not the case in FE11).
So, how does it function? No, really. Because bodily resurrection of the dead is one of those metaphysical conundrums that distresses, say, professional theologians. How's that work? If we accept that the half-explanation Claude gives for the Valkyrie Staff in FE4 applies to the Aum (damn you, Tiltyu!), then everyone is born with a life force/essence, and this is the key to resurrection. As the life force thing is a staple of FE games, it seems fair to assume this holds true for Archanea as well as Jugdral.
So, what do we know?
( Devil's in the details... )
2) The life essence of both earth dragons and divine dragons is so strong that they're extremely hard to kill in the "permanent" sense (Canon-- Medeus, Nagi, and Tiki if you don't recruit her in FE11 all are evidence here).
3) So, resurrecting a human being would seem to be a small-scale, deliberate equivalent of what dragons seem to do naturally-- rejoining the "essence" of the individual to the corporeal body... or a corporeal body, anyway. (Assumption)
4) Even for dragons, this isn't easy... after a dirt nap lasting about a century, Medeus isn't really himself and would seem to need a "boost" from the Aum staff to have the full powers of his physical body back (Canon from FE11). After being dead AGAIN for a couple of years, he would need the life forces of four (4) priestesses to get back into form (Canon, FE3)... and the ritual in that case would make him a Dark Dragon instead of his normal Earth Dragon self. (So here we have a case of a bad, icky, things-go-wrong resurrection, even in Archanea).
But again, what about people?
First off, "life essence" and souls. From what we can piece together, it appears Archanea has a heaven (death quotes for Linde and Lena, FE11) and a hell (death quote from Gharnef, FE11). The belief seems to be that people remain "themselves"-- the individual souls retain the sense of the self, and don't merge into some kind of hive or get recycled. (So, no, Marth is not a reincarnation of Anri.) Soul-merging or recycling would make this resurrection dealie very, very strange.
Elice tells Marth in FE11 that the Aum can be used to resurrect a "fallen comrade." What could we infer from this? Here are a few possibilities:
A) Just as healing magic doesn't seem to work on illnesses, resurrection magic doesn't work on deaths from natural causes. Perhaps the "life essence" of someone who dies a natural death is depleted through illness/infirmity. Then again, what about someone who dies from an accident-- a child who falls out of a tree, a fisherman who drowns?
B) There's some kind of "justice" principle at work-- people who die in a holy cause in which they are actively participating rate better than people who just get crushed by falling masonry or killed for lulz. (Justice? Bleh.)
C) Life essence depletes after death, so someone killed three or four years ago (like Marth's father) can't be resurrected, but someone killed three or four months ago can be. (I used to think the inability to resurrect the "canon sacrifice" from FE11 was a evidence for this, but in light of FE12, it's not.)
D) Some people are just more special than others. People Marth happens to like are especially special, I guess.
So... if he'd really wanted to, could he have asked for Elice to bring back their mother? Liza, after all, while apparently a non-combatant, died a very unnatural death at the hands of the bad guys, and presumably being the mother of the Chosen One would give her a spiritual edge over random nobodies. I realize you can't do that for game mechanic reasons, but still-- would it have been possible? Also, would it have been possible for Marth to pull a Lyon and bring Cornelius back so that Dad could deal with that dragon problem? What would have happened if they'd tried it?
OK. So those are just some of the questions affecting the spiritual side of resurrection. Now, what about the body?
Well, what becomes of bodies in Archanea? Per FE2, the custom among some of the people, under some circumstances, is to wrap the dead in a sheet, toss them in the ocean, and let the current bear them away. So, unless you're lucky enough to get washed up on a foreign shore and revived by a hot priestess, you're fish food. I doubt that's the custom on the mainland, though. Cremation, earth burial, mummification, something else entirely... we don't know. If the legend of resurrection was passed down in some form via religion, people might take care to keep bodies intact, disposing of them in the earth or the water without any mutilation or evisceration. And, in some cases, without even a decent post-mortem examination.
Wartime dead might not be that fortunate, though. Shot, stabbed, cleaved in two, decapitated, fried, frozen, incinerated, devoured by swarms of insects, crushed by projectiles, flattened in fall from a pegasus, mauled and/or eaten by a manakete... there's a lot of ways to die that would leave the body in terrible shape, even if a resurrection could be performed immediately after the battle. To say nothing of resurrecting someone who's been worm food or fish food since, say, Galder Harbor. Yet, this is entirely possible, which raises a new question. A really... interesting one.
Is the body the same physical form the soul once inhabited? Does the Aum spell create a new, intact, uncorrupted body for the life essence to be joined with? In other words... are we treading into morph territory?
Resurrection in Magvel (a Bad Thing) definitely involves reanimating the original body of the deceased, which leads to things like zombie!Monica. In this case, the soul of the deceased may not even be present-- their mind/personality certainly is not. Then again, if the zombie brain is basically mush, how would the mind make its presence known? Yech.
But we honestly can't tell from what's given us in Archanea if the resurrection involves reanimation of the deceased or the materialization of a healthy new body. If the former, how does the healing mechanic work? If the latter, when Elice does her thing in the middle of battle, do we end up with two bodies-- the still-warm dead one, and the new living one? Does the new body age at the same rate? Is it fully-functional (not sterile)?
This whole thing raises so many questions that it might be a good thing that the Aum is not standard-issue FE equipment. The holiest magic looks awfully unholy if you think too long over it.