@vangoz I've always assumed Idaten are functionally immortal, since the moment they're brought into life they're already physically aged appropriately and even in full attire. The reason they appear "aged" like the previous generation is simply their personal acknowledgment of how long they've been alive and their form reflects that in the same way they can manifest anything else about themselves.
@sirflimflam The new generation of Idaten pop into existence as adults from the start, but Rin was actually a child 800 years ago when the older Idaten were around, and the older Idaten expected that they would pass in time (see chapter 11). This means that there was a sort of "lifespan" for older Idaten up to Rin, and there was some sort of "growth" affecting Rin, that somehow no longer applies to the current generation of Idaten.