Within the theory of ion channeling in single crystals the so-called rule of reversibility claims equal probabilities for de- and rechanneling. However, the experimental study of this work shows a strong violation of this rule. Specially developed computer simulations provide the explanation of this unexpected behavior in terms of a hysteresis of the mean ion charge state during the ion's motion along lattice directions. This sheds new light on the process of charge exchange of heavy ions in solids.