An electron injector concept for a laser-plasma accelerator was developed by E. Esarey et al. [Phys. Rev. Lett. 79, 2682 (1997)] and G. Fubiani et al. [Phys. Rev. E 70, 016402 (2004)] ; it relies on the use of counterpropagating ultrashort laser pulses. In the latter work, the scheme is as follows: the pump laser pulse generates a large-amplitude laser wakefield (plasma wave). The counterpropagating injection pulse interferes with the pump laser pulse to generate a beatwave pattern. The ponderomotive force of the beatwave is able to inject plasma electrons into the wakefield. In this paper, this injection scheme is studied using one-dimensional Particle-in-Cell simulations. The simulations reveal phenomena and important physical processes that were not taken into account in previous models. In particular, at the collision of the laser pulses, most plasma electrons are trapped in the beatwave pattern and cannot contribute to the collective oscillation supporting the plasma wave. At this point, the fluid approximation fails and the plasma wake is strongly inhibited. Consequently, the injected charge is reduced by one order of magnitude compared to the predictions from previous models.