The effect of the spherically symmetric caging field on the asymptotic time behavior of the geminate recombination (GR) kinetics is explored. Time-dependent solution of the Smoluchowski equation with the Coulomb potential and the spherically symmetric linear caging potential is derived. The asymptotic kinetics is characterized by the nonuniversal exponent, which increases linearly with the field for weak fields. The deviation from the universal diffusion-controlled kinetics k(t) approximately t-3/2 is due to the "finite volume" effects. The model can mimic the many-body effects on GR kinetics. Its possible use for the interpretation of the recent experimental data on the pH effect on the long-time GR kinetics is discussed.