We report a study of the role of electron scattering at acoustic and polar optic phonons for Bloch gain of a terahertz radiation in semiconductor superlattices of different miniband widths. A three-dimensional Monte Carlo method was employed to calculate the dynamic mobility of miniband electrons in GaAs/AlAs superlattices subject to both static and high-frequency fields at low temperature (4 K); Bloch gain is indicated by a negative real part of the dynamic mobility. We found that for a superlattice with a miniband width smaller than the optic phonon energy (36 meV), scattering of electrons at acoustic phonons alone mediates the formation of electron bunches in momentum space and introduces gain, while for larger miniband widths, optic phonon scattering is dominant for gain. Due to a decrease of the energy-relaxation time of the miniband electrons, the alteration of the superlattice miniband width from smaller to larger magnitude, with respect to the optic phonon energy, results in broadening of the resonancelike dynamic mobility curve and considerable extension of the frequency range for the strong Bloch gain. The study delivers criteria for the observation of the Bloch gain.