I'm at work, so can't write super detailed response. But I think the fallacy of your comparison is the assumption that Nidhogg and Midgardsormr actually died. They didn't. Thordan's knights even admit that they merely drove off Nidhogg after prizing both his eyes. They knew without them he was powerless and would die of his wounds. Midgardsormr exploded but his eyes remained and his broken body went into slumber to recover.
We know of two of the Seven Celestial Wyrms who actually died. Ratatoskr and Bahamut. Ratatoskr's body was ripped asunder and her eyes devoured. You can find the remains of her lifeblood at Tharl Oom Khash. We don't know how Bahamut was slain by the Allagans, but we know the Ascians helped them. I can only assume it was in such a way that destroyed both his eyes.
I think for one of the Seven to truly die, their eyes must be destroyed like Ratatoskr's. Haldrath kept Nidhogg's eyes safe. Therefor he can never truly die.
(I will come back later and link sources and such, but hope this helps! ^^ )
We know of two of the Seven Celestial Wyrms who actually died. Ratatoskr and Bahamut. Ratatoskr's body was ripped asunder and her eyes devoured. You can find the remains of her lifeblood at Tharl Oom Khash. We don't know how Bahamut was slain by the Allagans, but we know the Ascians helped them. I can only assume it was in such a way that destroyed both his eyes.
I think for one of the Seven to truly die, their eyes must be destroyed like Ratatoskr's. Haldrath kept Nidhogg's eyes safe. Therefor he can never truly die.
(I will come back later and link sources and such, but hope this helps! ^^ )