We consider a mean magnetic induction fieldBevolving in an electrically conducting turbulently convecting fluid sphereV, where gravity acting radially is the only force imposing order. The turbulence is radially stratified and mirror-symmetric about planes through the origin. The only possible mean flow is spherically symmetric and radial. For small-scale turbulence, a large-scale mean field emf is generated that to a good approximation is linear inBandVB.This emf comprises the spherically symmetric β1, β2, γ1and δr1effects of Rädler (1980). In combination with the molecular magnetic diffusivity ηm, these effects produce anisotropic diffusion, different for poloidalSand toroidalTmagnetic fields, and characterised by generalised diffusion coefficients ηi(i= 0, 1, 2). The γ1and δr1effects also produce field generation similar to induction by a radial compressible laminar flow or equivalent (e.g. thermomagnetic) effect. Reasoning that usually ηi> 0, we prove decay of the norms max|r2Br| and ||T/r||1,v. For each of these norms, we give a bounding function that decays exponentially with a prescribed decay rate. Furthermore, the decay of each norm is strictly monotonic, regardless of time variations in the generation or diffusion terms. We infer that a self-exciting mean field dynamo cannot persist unless some mechanism, such as rotation, is present to break either the spherical or mirror symmetry of the turbulence. For low conductivity (large ηm) or strong turbulence (large β1), and relatively weak anisotropy (smaller β2, δr1) the decay occurs on the total diffusion time-scale determined by ηm+ β1In stars where β1probably dominates, the decay is therefore very fast on the molecular diffusion time-scale. In such cases rotation is an obvious choice for symmetry-breaker, and possible field maintenance.