This question already has an answer here:
- Are Fidelius charms stackable? 1 answer
If they knew the place was compromised with Snape knowing its location and the Order thinking him a traitor, why didn't someone just remove and recast the Charm? Obviously, we know that he didn't tell the Death Eaters. The idea that how to cast the Charm isn't widely known doesn't hold weight either as someone within the Order cast the Charm on Shell Cottage. Unless they specifically had to learn it for that, but at the same time, the same logic applies, why didn't they just do that for Grimmauld Place?
For that matter, a Fanfic that I read that was released after HBP figured the idea out. Even if it was going on the original logic that if the Secret Keeper (or the caster, can't remember which.) dies, the Charm cancels out. I guess that Hermione was right, Wizards really don't use Logic a lot do they? But I'm surprised that Hermione didn't come up with the idea herself for that matter.