Like any storm, once a hurricane is separated from its source of fuel, it dies.
The storm's basic fuel is warm, evaporating sea water. Most hurricanes die out after moving over cooler water or land where they can no longer feed off the warm water. Hurricanes are also threatened when they move into a more typical storm environment. The mid-level winds that feed general thunderstorms, for example, tend to rip apart a hurricane, severing the circulation of rising and sinking air that keeps the storm churning. Sometimes, a hurricane can be killed by another hurricane, which shears apart the smaller storm and absorbs some of its energy.