Does Earth's magnetic field arise from a fission reactor in its core?
The conventional explanation for the Earth's magnetic field is that some combination of differential rotation and/or convection occurs in the Earth's outer core, primarily in molten iron-nickel (+ sulphur, hydrogen etc.), which acts as a kind of dynamo. Whilst we can't prove it by direct observation, this seems an eminently plausible mechanism. If this is true, then the heat of the core will eventually dissipate, resulting in freezing of the core and cessation of the Earth's magnetic field. The existing heat is partly primordial and partly radiogenic from the decay of U, Th and K, and will take many billions of years to dissipate. 

The georeactor hypothesis requires a critical mass of uranium at the centre of the Earth to start up and maintain a nuclear reaction. There are two reasons why this hypothesis is seldom taken seriously except by Herndon himself. Firstly, in order for uranium to reach criticality it has to be a very high concentration of uranium. There is no known concentration mechanism which could achieve this in the Earth's core, whereas there are many reasons to believe that the uranium would be dispersed or 'poisoned' by lead and other heavy metals. Whilst the pressure at the Earth's core would be immense, gravitational separation, i.e. density fractionation, would be almost non-existent. Secondly, if this hypothesis was correct we would expect to see a huge flux of anti-neutrinos in such detectors as the super Kamiokande. We don't. So I'm not losing any sleep at the prospect of the Earth losing it's magnetism within the next billion years.