The Fidelius Charm is not without its weaknesses. If the Secret Keeper wishes to do so, they may divulge the information at any time (although the secret cannot be forced, bewitched or tortured out of a Secret Keeper who does not wish to give up their secret; it must be given voluntarily). If the Secret Keeper dies, anyone to whom he or she has confided the information will become a Secret Keeper. This could involve many people, any of whom might be more willing to share the secret.
Generally speaking, being a Secret Keeper is a dangerous position to occupy. It is such a serious and binding enchantment that few would undertake it lightly. In spite of the fact that the secret can only be given up voluntarily, many have been subjected to the Imperius and Cruciatus Curses in an effort to make them share their information.