In this work, a nonlinear variational linear combination of atomic orbitals scheme we introduced recently (Lima et al 2007 Phys. Rev. B 75 073201) for studying hydrogenic systems in semiconductors is adapted for the computation of the effect of a high-frequency, intense laser field on the positronium (Ps) quantum states. Our nonperturbative approach, based upon the Kramers-Henneberger translation transformation, allows us to show that, for sufficiently high intensities, the radiation field induces a wavefunction dichotomy, which causes a reduction on the positronium decay probability (i.e., enhances its lifetime). Our results point out that an enhancement of up to four orders of magnitude in the Ps lifetime can be attained with the current laser technology. Our careful quantitative analysis also corrects some mistakes in the approximate formulae proposed by Ehlotzky in a previous work (Ehlotzky 1988 Phys. Lett. A 126 524).