  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.
