The Markov, as well as the secular approximations, are key assumptions that have been widely used to model decoherence in a large variety of open quantum systems, but, as far as intermolecular collisions are considered, very little has been done in the time domain. In order to probe the limits of both approximations, we here study the influence of pressure on the alignment revivals (echoes) created in properly chosen gas mixtures (HCl and CO2, pure and diluted in He) by one (two) intense and short laser pulse(s). Experiments and direct predictions using molecular dynamics simulations consistently demonstrate, through analyses at very short times (< 15 ps) after the laser kick(s), the breakdown of these approximations in some of the selected systems. We show that the nonadiabatic laser-induced molecular alignment technique and model used in this study directly provide detailed information on the physical mechanisms involved in the collisional dissipation. Besides this "fundamental" interest, our findings also have potential practical applications for radiative heat transfer in planetary atmospheres and climate studies. Indeed, short time delays in the dipole autocorrelation function monitoring the light absorption spectrum correspond to large detunings from the optical resonances in the frequency domain, thus influencing the atmospheric transparency windows. Furthermore, the fact that the approach tested here for linear rotors can potentially be applied to almost any gas mixture (including, for instance, nonlinear and/or reacting molecules) further strengthens and broadens the perspectives that it opens.