Cognitive effort and self-control are exhausting. Although evidence is ambiguous, behavioural studies have repeatedly suggested that control-demanding tasks seem to deplete a limited cache of self-regulatory resources leading to performance degradations and fatigue. While resource depletion has indirectly been associated with a decline in right prefrontal cortex capacity, its precise neural underpinnings have not yet been revealed. This study consisted of two independent experiments, which set out to investigate the causal role of the right dorsolateral prefrontal cortex (DLPFC) in a classic dual phase depletion paradigm employing non-invasive brain stimulation. In Experiment 1 we demonstrated a general depletion effect, which was significantly eliminated by anodal transcranial Direct Current Stimulation to the right DLPFC. In Experiment 2, however, we failed to replicate the basic psychological depletion effect within a second independent sample. The dissimilar results are discussed in the context of the current 'replication crisis' and suggestions for future studies are offered. While our current results do not allow us to firmly argue for or against the existence of resource depletion, we outline why it is crucial to further clarify which specific external and internal circumstances lead to limited replicability of the described effect. We showcase and discuss the current inter-lab replication problem based on two independent samples tested within one research group (intra-lab).