You mean like how the Baroness sacrificed children to retain her youth?
'Like' in the sense that it was a magic ritual by a mage for a mage, not in the 'their immortality is powered by the blood of babies.' Immortality could easily have been an elite-only thing- same with the endless sleep.
That said, so far all the promising avenues towards life extension have been via blood magic. Tevinter, Warden, and even Dalish mages have been able to bolster life forces and extend their life spans unnaturally via it. It wouldn't be out of place if Arlathan did the same via the same, nor would it be out of place if it had been a less than equal bearing of costs in a less than equal political environment.
It wouldn't explain how human contact ruined it, but then nothing about the human influence makes sense as a cause. Humans may not even have been the cause, but rather a correlation. The difference between elves and humans seems to be magical in nature, given Gaider's comments on human-elf mixing.
Personally, I wouldn't be surprised if Humans were an offshoot from the elves, a sort of 'losing magic' trait that got progressively more common. That could tie into the primevial history about the pre-Veil, when everyone may or may not have been magical and magic. If there was ever a time all the elves had magic, I'd wager it was then, and lost with the Veil.
It could have been something like
Pre-Veil: Dragons Rule the Sky, Magic Runs Free, Gods Run Ramptant, Etc. Because of all the magic running everywhere, elves are formed from the magic infusing everyone. Magial immortality is at its peak.
The Veil forms. Possibly naturally, possibly deliberatly to contain something in the Fade. With the separation from the Fade, only the people lucky enough to have a way through are able to keep using magic: these are the first (elven) mages, who go on to rule the mageocracy of Arlathan. Natural/old magics begin to fade: the immortality magics (whatever they are) begin weakening.
The first humans start to appear in distant, uncivilized reaches. Rather than a new species, they could be in fact elves who lost the magical infusion in their being. As a consequence of their lack of magic, other elves who breed with them also have their children lacking magic.
Humans arrive around the time the magics begin to fade. Correlation is considered causation, even though the Veil itself is to blame for both. Humans are tribals, but the decline of the original magics leads to the decline of Arlathan.
Begin recorded history with the Tevinter Imperium rising as a power.