We have investigated resonant tunneling through impurity states with large binding energy of the GaAs/ AlAs double-barrier resonant tunneling heterostructure. These states originate due to the penetration of Si impurity atoms from the heavily doped emitter layer that is adjacent to one of the two AlAs layers. Magnetotunneling transport results demonstrate that resonant peaks and steps arise due to tunneling through the X-valley-related donor states localized in an AlAs layer. The strong asymmetry of the doping profile in our structures provides substantial accumulation of the resonant electrons at one bias polarity, which gives rise to the intrinsic bistability observed for the impurity-assisted resonant tunneling. Using perturbation theory, we estimated the value of the current and tunneling rates through the X-valley-related donor states, which is in good agreement with the measured current value and the registered bistability effect. Observed Zeeman splitting of the current peak allowed us to determine the value of the g factor of the confined impurity states.