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High-order-harmonic generation (HHG) by atoms in a strong laser field is analyzed theoretically, taking into account atomic potential effects beyond the strong field approximation (SFA). Our analytical derivation extends the time-dependent effective range (TDER) theory, developed previously for a short-range potential supporting only a single bound state, to the case of a potential supporting two bound states having different angular momenta and dynamically interacting with the continuum. In contrast to the SFA and the single-state TDER model, in both of which the HHG rates in the region of the high-energy plateau cutoff involve only the plane-wave (first Born) approximation for the photorecombination cross section, our analytic expression for the HHG rates in the two-state TDER model involves the exact photorecombination cross section for this model. These results justify the factorization of HHG rates in the high-energy plateau region in terms of the electron wave packet and the exact (non-Born) photorecombination cross section, which was suggested previously using only phenomenological arguments.