Broadband satellite communication networks, operating at Ka band and above, play a significant role to worldwide telecommunication infrastructure, providing backhaul and direct-to-user satellite services. Rain attenuation at these frequencies is the most dominant impairment factor that degrades the performance of the system. The dynamic reconfiguration of multi-beam satellite antennas has recently been proposed as a fading mitigation technique. In this paper, the problem of finding the power allocation among the beams of such an antenna, aiming that the number of subscribers not receiving the desired quality of service is minimized is addressed for a satellite communications system with a GEO satellite serving fixed earth terminals. An algorithm for the dynamic power allocation using a physical-mathematical model for rain attenuation prediction is proposed. Extended simulation results highlight the improvement of the dynamic scheme over the static allocation based on long term rain attenuation characteristics.