  Instability of quantum anomalous Hall (QAH) effect has been studied as
function of electric current and temperature in ferromagnetic topological
insulator thin films. We find that a characteristic current for the breakdown
of the QAH effect is roughly proportional to the Hall-bar width, indicating
that Hall electric field is relevant to the breakdown. We also find that
electron transport is dominated by variable range hopping (VRH) at low
temperatures. Combining the current and temperature dependences of the
conductivity in the VRH regime, the localization length of the QAH state is
evaluated to be about 5 $\mu$m. The long localization length suggests a
marginally insulating nature of the QAH state due to a large number of in-gap
states.
