The paper reconsiders the problem of the mixed convection boundary layer flow near the lower stagnation point of a horizontal circular cylinder with a second order slip velocity model and a constant surface heat flux studied recently by RoKa et al. (2013). The ordinary (similarity) differential equations are solved numerically using the function bvp4c from Matlab for different values of the governing parameters. It is found that the similarity equations have two branches, upper and lower branch solutions, in a certain range of the mixed convection parameters. A stability analysis has been performed to show that the upper branch solutions are stable and physically realizable, while the lower branch solutions are not stable and therefore, not physically possible. This stability analysis is different by that presented by RoKa et al. (2013), who have presented a time-dependent analysis to determine the stability of the solution branches.