Simple analytical expressions are obtained for the escape factor for low-energy electrons in an atomic plasma at intermediate and high values of the reduced electric field in the near-cathode region, when the dominating electron energy losses are due to inelastic collisions of electrons with atoms. An approximate account of the reflection of electrons by the cathode surface is introduced. Calculated escape factors are in reasonable agreement with the results of the Monte Carlo simulations available in the literature. When applied to cathodes of high-pressure arc discharges, the obtained results indicate that the escape factor is close to unity in cases where the near-cathode space-charge sheath is collision-free or moderately collisional. If the sheath is collision-dominated, the escape factor may be different from unity; for example, this is the case under conditions of a 100 bar mercury plasma of a mercury arc lamp.