There seems to be some evidence that suggest it can get eradicated if all fish gets immune to it and no new fish (or ich strains) are added for a extended period of time.
Although I have read similar, the logic of this makes no sense to me. If the resident fish were truly immune, then logically the ich parasite would die out in the same way it would if the tank were fishless - 72 days, give or take - yet it does not. If it is even true that ich dies out over a longer period of time (I've not observed this to be the case) it must be that the fish are immune enough to resist getting overwhelmed by the parasite but not to avoid some level of infection. That a single strain might die out must have something to do with limited genetic pool.