We have studied suspensions of hard-magnetic BaFe12O19 particles in water, ethanol and 1-butanol. The surfaces of these particles were previously modified with the surfactant dodecylbenzylsulphonic acid. The stabilities of the suspensions were estimated from their saturation concentrations and zeta potentials. We found that the 1-butanol suspensions were more stable than the ethanol-based suspensions and much more stable than the water-based suspensions. We analyzed the suspensions and the dispersed particles using gravimetry, conductometry and transmission electron microscopy, measured their zeta potentials, and calculated the interparticle-attraction interaction energies due to the van der Waals and magnetic dipole-dipole forces. The magnitudes of the attraction energies varied significantly with the particles' sizes and the separation distances between the particles, and we found that the contribution of the van der Waals attraction energy can be neglected with respect to the magnetic dipole-dipole attraction. The observed differences in the stability of the suspensions were explained on the basis of the calculated electrostatic and steric repulsion energies. Electrosteric stabilization was possible in the 1-butanol and the ethanol for particles with radii and thicknesses up to 15 nm, while a too small electrostatic repulsion and the absence of steric repulsion in the water resulted in rapid agglomeration.