In supersymmetric models, very heavy stop squarks introduce large logarithms into the computation of the Higgs boson mass. We calculate three- and four-loop next-to-next-to-leading-log corrections to the Higgs mass and compare the fixed order formulas numerically to the resummation results in order to estimate the range of supersymmetry scales where the fixed-order results are reliable. We find that the four-loop result may be accurate up to a few tens of TeV. We confirm an accidental cancellation between different three-loop terms and show that it persists to higher scales and becomes more effective with the inclusion of higher radiative corrections. Existing partial three-loop calculations that include only one of the two cancelling terms may overestimate the Higgs mass. We give analytic expressions for the three- and four-loop corrections in terms of Standard Model and the soft SUSY breaking parameters, and discuss what happens for low values of the CP-odd Higgs mass.