It is experimentally demonstrated that, if the areas of the reading pulses are small, the relaxation decay of the long-lived photon echo in a LaF3:Pr3+ crystal (the H-3(4)-P-3(0) transition, lambda = 477.7 nm, and T = 2.2 K) does not depend on the number of reading pulses. It is theoretically shown that this effect holds for both conventional and accumulated long-lived photon echo in Van Vleck paramagnetics.