In an absorptive plasma, damping of radiation mechanisms can influence the bremsstrahlung formation in case of large radiation formation lengths. We study qualitatively the influence of this effect on the gluon bremsstrahlung spectrum off heavy quarks in the quark-gluon plasma. Independent of the heavy-quark mass, the spectrum is found to be strongly suppressed in an intermediate gluon energy region which grows with increasing gluon damping rate and increasing energy of the heavy quark. Thus, just as polarization effects in the plasma render the bremsstrahlung spectra independent of the quark mass in the soft gluon regime, damping effects tend to have a similar impact for larger gluon energies.