  We treat small trapped unequal-mass two-component Fermi gases at unitarity
within a non-perturbative microscopic framework and investigate the system
properties as functions of the mass ratio $\kappa$, and the numbers $N_{1}$ and
$N_2$ of heavy and light fermions. While equal-mass Fermi gases with infinitely
large interspecies s-wave scattering length $a_s$ are universal, we find that
unequal mass Fermi gases are, for sufficiently large $\kappa$ and in the regime
where Efimov physics is absent, not universal. In particular, the
$(N_1,N_2)=(2,1)$ and $(3,1)$ systems exhibit three-body (3b) and four-body
(4b) resonances at $\kappa = 12.314(2)$ and $10.4(2)$, respectively, as well as
surprisingly large finite-range (FR) effects. These findings have profound
implications for ongoing experimental efforts and quantum simulation proposals
that utilize unequal-mass atomic Fermi gases.
