The energy scale dependence of the Sivers asymmetry in semi-inclusive deep inelastic scattering is studied numerically within the framework of TMD factorization that was put forward in 2011. The comparison to previous results in the literature shows that the treatment of next-to-leading logarithmic effects is important for the fall-off of the Sivers asymmetry with energy in the measurable regime. The TMD factorization based approach indicates that the peak of the Sivers asymmetry falls off with energy scale Q to good approximation as 1/Q0.7, somewhat faster than found previously based on the first TMD factorization expressions by Collins and Soper in 1981. It is found that the peak of the asymmetry moves rather slowly towards higher transverse momentum values as Q increases, which may be due to the absence of perturbative tails of the TMDs in the presented treatments. We conclude that the behavior of the peak of the asymmetry as a function of energy and transverse momentum allows for valuable tests of the TMD formalism and the considered approximations. To confront the TMD approach with experiment, high energy experimental data from an Electron–Ion Collider is required.