In supersymmetric models extended with an anomalous $U(1{)}_{H}$ different $R$-parity violating couplings can yield an unstable neutralino. We show that in this context astrophysical and cosmological constraints on neutralino decaying dark matter forbid bilinear $R$-parity breaking neutralino decays and lead to a class of purely trilinear $R$-parity violating scenarios in which the neutralino is stable on cosmological scales. We have found that among the resulting models some of them become suitable to explain the observed anomalies in cosmic-ray electron/positron fluxes.