The Arrhenius equation may not account for the temperature effect on thermal inactivation rate constants. Why can the thermal inactivation kinetics not be expected to follow Arrhenius? The reason that the inactivation constants do not follow Arrhenius is it because of other chemical processes occuring like diffusion?
Without attempting to elaborate (this is not my area of expertise) I rely on the abstract to an article  reviewing the subject for an answer:
The Arrhenius equation has been widely used as a model of the temperature effect on the rate of chemical reactions and biological processes in foods. Since the model requires that the rate increase monotonically with temperature, its applicability to enzymatic reactions and microbial growth, which have optimal temperature, is obviously limited. This is also true for microbial inactivation and chemical reactions that only start at an elevated temperature, and for complex processes and reactions that do not follow fixed order kinetics, that is, where the isothermal rate constant, however defined, is a function of both temperature and time.
 Peleg et al Critical reviews in food science and nutrition 52(9):830-51 (2012)