Apparatus, and an associated method, that reduces the occurrence of generation of redundant requests for retransmission of packet-formatted data, formatted at a physical layer and at a higher-logical layer, such as at an RLP layer. An estimate of an appropriate delay period is formed. The estimate is responsive to communication conditions in the communication system. When a data packet appears to have been inadequately delivered to the RLP logical layer, a DELAY_DETECTION_WINDOW timer is caused to time out the delay period estimated by the estimator. The request for retransmission, generated at the RLP layer, is permitted, upon expiration of the timer if the data packet has not yet been successfully delivered to the RLP layer and the transmitter has not given up the data packet delivery.