The site today is just text with a simplistic search engine attached. This make relocating them very simple, duplication very simple, and running it very simple. Because the site is that simplistic, removing it gets that much harder. Its like trying to remove illegal numbers from the internet, and expecting that one large raid on the number central will do it.
What lobbyist are trying to do is takeing the site down through DNS by getting TLD's responsible for the internet at large. This is a bad idea(tm), and is being pushed against by the TLD's. It would also not work.
So, the Pirate Bay's servers are in countries that either don't care to enforce or aren't able to enforce copyright law.
This resistance to physical attacks is why countries eventually started blocking it at the consumer end, through ISP-enforced bans.
It's a shame they can't talk more openly about it, I'm sure they could teach some valuable lessons in reliability.