The radiation of an accelerated or a decelerated charge particle is called "Bremsstrahlung" radiation, which means (roughly) deceleration radiation. The radiation is a continuous spectra. i.e. it's not the emission of one photon. The charged particle which is accelerating emits continuously photons of different energy depending upon the rate of change of it's own energy at that instant.
Now the question is, where does this energy come from? In case of deceleration it is obvious that the kinetic energy of the charged particle is giving rise to the radiation energy. What about accelerating particle? Well, the energy used by the agent to accelerate the charge actually is used in two ways. One part increases it's kinetic energy, the other produces the radiation.
So in your case, when the ionised gas is accelerating for hours it emits radiation continuously, of course the radiation becomes visible only when the acceleration is sufficiently large which is very close to the star or whatever is accreting it.
P.S. Just for fun,consider this extra thought. Einstein's General relativity says that an accelerated frame is completely equivalent to a frame exposed to gravity. But if there is a charge in accelerated frame it should radiate. Does that mean that all static charges in earth radiates?