The stability of the ground and excited states of Positronium-atom complexes [A, Ps], Ps=[e(+),e(-)], has been explored for A=Li, B, C, O, F using variational and diffusion Monte Carlo techniques. From the numerical results of our simulations it turns out that the ground state of the complexes [Li, Ps]S-2, [C, Ps]S-3, [O, Ps]P-1, and [F, Ps]S-2 is stable against the break up in the two neutral fragments a and Ps, while the ground state of [B, Ps]P-2 has an energy above the same dissociation threshold. As to the excited states, the only possible candidate, [F, Ps]P-2, has a total energy statistically equal to the lower dissociation threshold, i.e. it does not seem to be stable against the dissociation.