Axion inflation is an attractive particle physics model of inflation with a rich phenomenology, due to the parity violating production of gauge-fields in this model, which may have implications for the production of gravitational waves, scalar perturbations and the baryon asymmetry. In recent years, a scenario with strong back-reaction of the gauge fields onto the inflaton in this model has been studied extensively, using different methods such as lattice simulations, solving the system numerically in Fourier space, or a novel technique called the gradient expansion formalism. Additionally, a well known analytical solution to Axion inflation exists. In this so-called Anber-Sorbo solution, the gauge field production counter-acts the scalar potential gradient, which may be too steep to allow for traditional slow-roll inflation. Our aim is to study the lifetime of the Anber-Sorbo solution using the gradient expansion formalism, motivated by a recent analytical calculation based on this solution. We initially rely on the approximation of a constant Hubble parameter used in the analytical study, but then make use of the full power of the gradient expansion formalism to examine the impact of a varying Hubble-rate. We find that the lifetime of the Anber-Sorbo solution can be extended to several e-folds at the cost of a high degree of fine tuning of the initial conditions.