Advanced Modular Reactors (AMRs) are expected to aid in the transition to net-zero emissions. In some candidate AMR concepts, a molten salt/fuel mixture passes through fuel channels in graphite bricks, while other bricks are reserved for the insertion of control rods. The neutron fluence in the reactor core displaces carbon atoms in the graphite, leading to a non-linear change in brick dimensions. This change in dimensions could, in certain circumstances, prevent the insertion of control rods and lead to reactor control failure. This paper explores how the exposure of graphite to radiation could lead to reactor control failure using both deterministic and probabilistic analyses. The deterministic approach determines the change in brick dimensions in a single channel using finite element analysis. Conversely, the probabilistic analysis uses a response surface surrogate Monte-Carlo analysis to predict the likelihood of reactor control failure for a single or multiple channels. The deterministic assessment indicates that reactor control failure is not likely. However, the probabilistic analysis shows that the epistemic and aleatory uncertainties in the reactor aggregate, leading to imperfect tessellation of the graphite bricks and a higher probability of failure. The probabilistic approach suggests that after 10 years, reactor control failure is likely in the outer core channels where the influence of imperfect tessellation is the strongest.