The possibility to generate a combustion transient of a composite AP.HTPB/86.14 propellant, burning under steady state conditions, was experimentally demonstrated by using a CO2 laser energy pulse. The experimental results point out that the burning propellant behavior can be defined by the curves separating, for every operating pressure, the continuous burning from the extinction solutions. In this paper, a simplified theoretical approach gives a phenomenological explanation of the energy pulse effect on the combustion process and the consequent burning propellant response after the deradiation transient. In the framework of this study the extinction condition is formulated in terms of the minimum temperature that causes the burning propellant to quench at the Pressure Deflagration Limit. The proposed theoretical work is aimed, first of all, to determine the critical radiant flux values, for different operating pressures, below which the burning propellant extinction is never achieved even if the laser pulse duration tends to infinity. Then, the extinction boundaries are defined choosing two different approximate approaches that take into account the ratio between the condensed phase relaxation time and the radiant energy pulse duration. Two limit cases, defined as slow/fast interaction of the radiant energy with the combustion process, can be used to describe the burning propellant extinction phenomena, and the results of this work indicate that the general trend of the computed boundary limits reproduces the experimental data.