  Quantum anomalous Hall (QAH) effect appears in ferromagnetic topological
insulators (FMTI) when a Dirac mass gap opens in the spectrum of the
topological surface states (SS). Unaccountably, although the mean mass gap can
exceed 28 meV (or ~320 K), the QAH effect is frequently only detectable at
temperatures below 1 K. Using atomic-resolution Landau level spectroscopic
imaging, we compare the electronic structure of the archetypal FMTI
Cr_0.08(Bi_0.1Sb_0.9)_1.92Te_3 to that of its non-magnetic parent
(Bi_0.1Sb_0.9)_2Te_3, to explore the cause. In (Bi_0.1Sb_0.9)_2Te_3, we find
spatially random variations of the Dirac energy. Statistically equivalent Dirac
energy variations are detected in Cr_0.08(Bi_0.1Sb_0.9)_1.92Te_3 with
concurrent but uncorrelated Dirac mass gap disorder. These two classes of SS
electronic disorder conspire to drastically suppress the minimum mass gap to
below 100 {\mu}eV for nanoscale regions separated by <1 {\mu}m. This
fundamentally limits the fully quantized anomalous Hall effect in
Sb_2Te_3-based FMTI materials to very low temperatures.
