We report detailed temperature and gate-voltage dependence of 1/f resistance noise in magnetically doped topological insulators (TI) Crx(Bi,Sb)2−xTe3. The noise is remarkably sensitive to the gate voltage, increasing rapidly as the chemical potential is moved towards the charge neutrality point. Unlike in identically prepared (Bi,Sb)2Te3 films, where mobility-fluctuations in the surface states is the dominant mechanism, the noise in the magnetic Crx(Bi,Sb)2−xTe3 originates from transport in the localized band tail of the bulk valence band. A strong increase in noise with decreasing temperature supports this scenario. At higher temperature (≥10 K), we observed large noise peaks at gate voltage-dependent characteristic temperature scales. In line with similar observations in other non-magnetic TI systems, we attribute these peaks to generation-recombination in the Cr-impurity band.