A) core hysteresis losses is the correct answer. The gain of a saturable reactor is limited primarily by core hysteresis losses. As the core material is cycled through its magnetic hysteresis loop, energy is lost due to the work required to magnetize and demagnetize the core. This energy loss manifests as heat, which reduces the overall efficiency and gain of the saturable reactor. The other options are incorrect because: B) inductive reactance in the control winding affects the control characteristics but not the gain, C) IR drop in the load winding impacts the output voltage but not the gain, and D) eddy current losses, while present, are typically smaller in magnitude compared to the core hysteresis losses.