  We examine the role of ionizing radiation emitted from black holes (BHs) in
suppressing the growth of the Rayleigh-Taylor instability (RTI) across the
ionization front (I-front) that forms when the gas fueling the BH is neutral.
We use radiation-hydrodynamic simulations to show that the RTI is suppressed
for non-accelerating fronts on all scales resolved in our simulations. A
necessary condition for the stability of the I-front is that the radius of the
Str\"omgren sphere is larger than the Bondi radius. When this condition is
violated the I-front collapses producing an accretion luminosity burst.
Transient growth of the RTI occurs only during the accretion burst when the
effective acceleration in the frame of reference of the I-front increases
significantly due to the rapid expansion of the Str\"omgren sphere.
