The transport and net loss of cyclotron radiation for burning plasmas represented by the ITER, FIRE and IGNITOR designs are assessed using the CYTRAN radiation transport code. Although cyclotron radiation might be expected to be a bigger issue in the higher field devices (FIRE and IGNITOR), the reference operating conditions in those devices are at lower temperatures so that the relative importance is nearly constant for all three. At the reference operating conditions for each of these devices, the net energy loss from cyclotron radiation is about 10% of the alpha power, and the axial loss is typically about 15% of the local alpha power density. If the same fusion power is generated at higher temperature and lower density than the reference operating points (as may be the case in advanced confinement modes), both the net and axial loss fractions strongly increase and are more competitive with other energy transport processes. The increase is much stronger for the high field devices where the axial loss can approach the local alpha energy production rate for T(0) ~ 30 keV. However, if the temperature increases at constant density (as in a thermal excursion), cyclotron radiation loss remains an almost constant fraction of the alpha production rate. This implies that it will not make a significant contribution to thermal stabilization. However, these and other calculations of cyclotron radiation transport are sensitive to assumptions of reflection, plasma geometry and profile shapes. Therefore, the effect of cyclotron radiation on operating conditions and burn dynamics will undoubtedly be a generic issue that any burning plasma will have to address.