User blog comment:Hyperborean/"The House of Hades" – official expectations blog/@comment-10750309-20130902134255/@comment-3146930-20130904005407

It is actually a bit of Self-Fulfilling-Prophecy when it comes to Frank's piece of wood. In the original story, Meleager's mother heard the Fates say that once a piece of wood in the fire went out, he would die. So his mother put out the fire and hid the wood. Years later, Meleager gave the prize for killing the Calydonian boar to Atlanta (a woman) which angered his father and brother...so he killed them. Anyway, as a result his mother tossed the wood in the fire so he died.

Frank has a similar case, as his life is tied to that piece of wood. If anything happens to it, he could die. However that isn't to say that the wood won't burst into flames when Frank is close to death, as they are linked together. If one dies/burns, they both die/burn.