Far more interesting is the toy called "Levitron". The top
in this toy spins without visible means of support.
In both toys there is no reason to expect dissipation to
occur due to induced currents. Induction requires a time
varying magnetic field, and these tops both spin about
their axes of magnetic symmetry. That is the reason there
is no dissipation - there is no motion of the field in
the case of smooth rotation.
The complex nodding behaviour* is best described in terms
of an oscillator with two degrees of freedom, I think.
The oscillator has two normal modes which are nearly
degenerate, and energy is coupled back and forth between
them at the beat frequency. I haven't done the analysis,
but casual observation strongly suggests that sort of
behavior to me.