By using the general theoretical framework proposed recently for treating the fluorescence quenching kinetics, we investigate the effect of light pulse intensity on the decay of fluorescence which follows excitation of fluorophors by the light pulse of very short but finite duration. It is seen that conventional theory breaks down when the exciting light pulse has a pulse width comparable to the fluorescent lifetime and its intensity is very high. We also find that even when the light intensity is not too high, conventional theory may fail in either of the following cases: (i) when the quencher concentration is high, (ii) when there is an attractive potential of mean force between the fluorophor and quencher, or (iii) when the energy transfer from the fluorophor to the quencher may also occur at a distance, e.g., via dipole-dipole interaction. The validity of the predictions of the present theory may thus be tested by fluorescence quenching experiments performed under such situations.