Hierarchical scheduling frameworks (HSFs) provide means for composing complex real-time systems from well-defined independently developed and analyzed subsystems. To support shared logical resources requiring mutual exclusive access in two-level HSFs, overrun without payback has been proposed as a mechanism to prevent budget depletion during resource access arbitrated by the stack resource policy (SRP). The same mechanism can be applied to support scheduling techniques, such as fixed-priority scheduling with deferred preemption (FPDS), that aim at a reduction of the architecture-related preemption costs and may improve the feasibility of a system. Whereas the blocking times and overrun budgets for shared logical resources will typically be much smaller than the normal budget, these values may significantly increase for scheduling techniques such as FPDS. In this paper, we therefor consider replenishment-bounded overrun, i.e. the overrun ends upon a replenishment, because the normal budget becomes available again, which allows for larger overrun budgets. We show that the global schedulability analysis for this special kind of overrun has a number of anomalies: (i) the usual theorem for critical instant does not hold, (ii) maximal blocking does not necessarily lead to a maximal response time, and (iii) it is not sufficient to analyse a fixed amount of time (say, a number of hyperperiods). We present analysis for two subsystems.