We have implemented a method based on the Feshbach formalism along with an explicitly correlated configuration interaction method to perform a systematic study on the behavior of resonance parameters (energies and lifetimes) of the autoionizing states of plasma-embedded He ${}^{1,3}{S}^{e}$, ${}^{1,3}{P}^{o}$, and ${}^{1,3}{D}^{e}$, as a function of the screening strength. In particular, we study the evolution of the lowest states in the series located below the He${}^{+}$($N=2$) ionization threshold in the unscreened case. At variance with one-electron atoms (where shape resonance widths vary monotonically with the screening strength) the evolution of the Auger width with respect to screening is found to be different for each series represented by ${(K,T)}^{A}$ pseudoquantum numbers until resonances merge into the upper electronic continuum, when crossing the He${}^{+}$(2$s$) threshold. We conclude from our ab initio calculations that, although resonances pertaining to the same ${(K,T)}^{A}$ series share a similar tendency in their widths against the screening strength, general propensity rules for the robustness of lifetimes, based on the isomorphic series in the ${(K,T)}^{A}$ classification, cannot be established in plasma-embedded helium.