Two-dimensional (2D) membranes based on perforated graphene have great potential in the field of separation of chemical species for a variety of applications, including gas treatment. In addition to recent experimental studies, several works simulate the mechanisms of gas permeation through this type of membrane using molecular dynamics, but few combine different techniques to ensure that their method of choice captures all relevant mechanisms. In particular, the re-crossing mechanism leading a gas molecule that has crossed the plane of the membrane to rapidly re-cross it in the opposite direction has never been documented. In this work, we study gas permeation through a simplified 2D membrane model. We combine equilibrium and non-equilibrium molecular dynamics simulations to quantify the impact of these re-crossing mechanisms on the values of the computed transport coefficients. Using non-equilibrium simulations as reference, we show that the equilibrium simulation techniques commonly used can lead to a significant overestimation of the transport properties of the membrane. We propose a simple method to probe the re-crossing dynamics during equilibrium simulations, making it possible to compute correct values of the transport coefficient without the need for non-equilibrium simulations. Furthermore, by analyzing the phenomenology observed in the simulations, we derive an analytical formula for the permeance that takes the form of an Arrhenius law with a non-trivial temperature dependent prefactor. In excellent agreement with our simulation results, this model provides a simple theoretical framework that captures the main mechanisms involved in gas permeation through 2D membranes, including the effect of re-crossing.