Positron annihilation lifetime spectroscopy measurements of polystyrene and poly(methyl methacrylate) have been performed at 20 K during ∼400 h. An increase of the probability of positronium (Ps) formation with irradiation time is observed. This effect is due to the accumulation of shallow‐trapped electrons which are stable at low temperatures. Detailed analyses of the lifetime spectra within the blob model framework show that these electrons induced by the previous positron tracks act as extra blob electrons: they either recombine with a cation or form Ps. This kinetic analysis introduced by the blob model indicates that no formation of Ps occurs after the blob recombination in these amorphous polymers. An increase of the free positron lifetime with the measuring time is also observed. This effect can not be explained in terms of artifact of discrete analysis caused by the existence of an ortho‐positronium lifetime distribution.