Consider how much of the storyline would be altered if Aerith did not die:
Aside from all the dialogue that speaks of Aerith in the past tense, there's the fact that if she were to live, going to speak with Bugenhagen during Disk 2 would be rendered unnecessary, going to the City of the Ancients after, as well, as would the search for the White Materia, in which Bugenhagen sends the party off to find the Key of the Ancients in order to activate the Ancient Machine in the City of the Ancients.
It was only after activating that machine that the party learned that the White Materia was glowing a pale green, meaning that Aerith's prayer had went through and the White Materia had already been activated.
It was also the above incident that allowed them to learn that Holy was activated, but wasn't moving because JENOVA/Sephiroth was holding it back.
Finally, the party learns that the Junon Canon had been moved and that Diamond WEAPON was approaching Midgar while still at the City of the Ancients, which immediately preceded the battle with Diamond WEAPON, the apparent death of Rufus Shinra, and the final showdown with the Shinra.
This being the case, a huge aspect of the storyline would be altered were Aerith still alive.
Finally consider that the ending itself would have needed to be altered, as she is not with the main party in the Northern Crater, nor on the Highwind, and only a ghostly image of her appears in the Lifestream during the ending. Also consider that her appearance in the Lifestream during the ending was meant to suggest that she was able to manipulate/convince the Lifestream to take action against Meteor.
Considering how much of the game would have needed to be altered, it's not at all possible for Aerith to be revived while preserving the integrity of the storyline itself.
To those who may argue that GameSharks allow for Aerith to be revived, and there is even a different line that she will say from the generic lines random other characters will say when in her place at that point (the "I'm sick of this" line -- which can be seen farther down -- after the snowboarding crash incident), keep in mind that GameSharks only alter existing memory that is on the discs. It's basically a scrambling of what is already there, not something that can create new aspects of the game, or be a key to the rest of its storyline. It should also be pointed out that the GameSharks don't provide access to any scene involving a revival of Aerith. They simply allow Aerith to be in the party when she shouldn't be, just as Sephiroth can be, as is shown in the pictures below:

That's why one can be at the Northern Crater on Disc 1. The entire game, in terms of environment and battle maps, was placed on the first disc, but the seperate discs were needed due to the FMV sequences taking up so much space. Being that Disc 3 contains both the Ultima WEAPON and the ending FMVs (which are longer than all the rest put together), it should be more than obvious that there's no extra space for FMVs depicting altered-versions of the ending, featuring Aerith in the Northern Crater with the party, or on the Highwind with them. In fact, Aerith being alive and being there would completely screw-up what
is in the ending, such as Cloud seeing Aerith's hand in the Lifestream, Cloud stating "An answer from the Planet... the Promised Land...I think I can meet her... there," and then Aerith appearing in the wake of the Lifestream just as Meteor was being destroyed.
Further, being that there wasn't even enough space to take into account in the FMVs that the player might do something as simple as recruit Vincent or Yuffie, it should be very obvious that no such thing would be done with Aerith.
While one might be able to argue that a revival of Aerith was intended -- which in itself is not supported, due to Nomura wishing for Aerith to die so that Tifa would become the main Female character of the game (as can be read on
this site) -- being that it wasn't included in the game, it's not part of the storyline canon. I would think that Aerith's continued state of being dead in Advent Children would be evidence enough in regard to this.
And contrary to popular belief, the International Version of FFVII did not include an Aerith revival.
The International Version (re-release in Japan, and first European release) is identical to the version that North America received, with the only exceptions being a few novelty items that are available within the game, such as Johnny's Jacket, and a bonus disk that came with the game in which vehicle schematics and concept designs were shown. While North America has been shafted in regard to International Releases ever since, with FFVII
it did get it in every capacity that relates to the game but the few novelty items. It was the first and only version released in North America.
As for Aerith's ultimate Limit Break, note that through level-whoring and making use of the Buggy supplied by Dio the player can acquire this before Aerith's death. Further consider that if Aerith were meant to be revived, or were meant to remain alive, that -- with her final Limit Break -- the latter Boss battles of the game would be made ridiculously simple.
Further note that the game's FMV sequences, including the one in which Aerith died and the ending FMV, were all made during 1995. They were the first things that were made aside from the script that the game would follow, made even before environment maps. The game wasn't released in Japan until January 31, 1997. The FMVs were completed for more than a year before the game was released, and the final version of the script was completed even before the FMVs.
Also, while on the subject of the script, when it was being written -- note that this was before the FMVs were even yet made -- Nomura made a phone call to the Director of the game (Yoshinori Kitase) and suggested that Aerith die and that Tifa become the game's heronine in her place, as they had never before had two heroines and then have one die. Mention of this matter can be found both
here and
here, and Nomura was originally quoted as saying this in a book entitled
Final Fantasy VII Kaitai Shinsho.
Essentially, being that an Aerith revival was not included in the game, that the FMVs in which she dies and the ending FMV in which her spirit appears amongst the Lifestream's energy were completed more than a year before the rest of the game, as was the script in which she would die due to Nomura's suggestion that Tifa become the main heroine, and that she is still dead in Advent Children, she died and remained dead in storyline canon, and there's no logical evidence that has ever been presented to suggest otherwise. Aerith was intended to die and remain dead.