Does someone know why Archdemons are immortal?

You will not be given any rational explanation when it comes to themes that concerns magic everything would just be a matter of suspension of disbelief.

The mechanics that revolve around the Archdemons as well as Corypheus are extremely far fetched and lack any fundamental basic rationale even if you are using the rules of Thedas because more often than not they contradict others rules created by the writers themselves.
Archdemons being able to reborn within darkspawns don't make sense on the light of the events of DAA,Corypheus being able to body jump in GW because "reasons"  also is never fully explained.


Edit i also noticed that the Mabari hound is tainted and could have been used to kill the Archdemon,but alas you don't have that option despite such option make sense.

The first warden should be more knowledgeable than the average wardens,as for him knowing about Flemeth's and Morrigan schemes suffice to say that in WH it was him who sent the HoF or the Orlesian warden after her,and if the HoF is alive it could easly tell him what they wanted to gain from the Archdemon,it's what my warden did since i have nothing to hide given the fact that i declined that "offer", the problem is of Morrigan not mine.

To my knowledge the dog is not cured from the taint,there is no cure for it it become resistant like the GW.
If cure the taint is as easy as just use a flower to do that than that will make all the population of Thedas look very stupid especially the warden who went in the Bermuda triangle for something that a Chasind Barbarian accomplished in a few minutes with just a flower.

The knowledge to delay the onset of Blight sickness through the use of herbs was apparently known to the Wardens for some time before the events of DAO. In fact the on-line Core Rule Book even claims that they can counteract it through herbs (suggesting even a partial "cure"). May be it is more a case that if you give the "anti-dote" quickly enough, it will stop the progress of the disease altogether, otherwise it merely slows it. It is said they learned this from the Dalish, although it is said their remedy will only stave it off for a time and eventually it will return and the sickness will kill the infected person. Hence Marethari being able to delay the onset in the Dalish Warden.

I'm pretty sure I read somewhere that it may have been elven slave recruits to the Wardens who originally came up with the Joining Ritual and may be even the theory of how to kill an archdemon. If it wasn't slaves then it may have been ancient writings (likely elvish) that gave them the clue. Given what we now know about the ancient elves, together with the beliefs of the Avaar, and the ability to return from death by reincarnation or simply possession of a willing subject, it is hardly surprising that the Wardens might have eventually worked out what was happeneing with the arch demon and how to prevent it.

This makes sense with DAO in isolation but not when you factor in all the later revelations concerning sentient darkspawn and Corypheus. This could either mean the writers hadn't really got the lore worked out when they wrote DAO, or we were denied certain knowledge because of spoilers for later storylines. Given how much a Dalish Inquisitor doesn't know about their own gods and customs, that they ought to know, coming from a culture that so values preserving and passing on their history, I think it may be a combination of the two why the lore concerning the reincarnation vs death of an archdemon now seems to make so little sense.

I do believe that is the reason,I doubt the concept of Corypheus or the Disciples existed when they made DAO.