A processor includes a plurality of input ports, memory circuitry for storing data blocks associated with protocol data units (PDUs) and received by the processor at the input ports, and controller circuitry coupled to the memory circuitry. The controller circuitry is operative to discard certain ones of the data blocks received at the input ports in an oversubscription condition in which the received data blocks exceed a designated capacity of the processor. A discarded data block indicator is generated for a given one of the input ports if a data block received at the given input port for a particular PDU is discarded. One or more additional data blocks received at the given input port for the particular PDU are discarded based at least in part on the discarded data block indicator. The oversubscription condition may thereby be overcome in a manner which advantageously minimizes the number of received PDUs that are corrupted through discarded data blocks.