The propagation of Dyakonov surface waves guided by the planar interface of (i) an isotropic dielectric material and (ii) a homogenized uniaxial dielectric composite material comprising both passive and active component materials was theoretically investigated, under the assumption that the optic axis of the uniaxial partnering material lies wholly in the interface plane. For a certain range of the volume fraction of the active component material, the uniaxial partnering material is neither wholly dissipative nor wholly active and the Dyakonov surface waves propagating in certain directions amplify but the Dyakonov surface waves propagating in other directions attenuate.