We consider a network of buffer-aided wireless devices having to transmit deadline-constrained data packets on a slotted-ALOHA random-access channel. While retransmission- based communication enhances reliability, the transmission of packets in the queue is delayed and as a result, they might get dropped before they are transmitted successfully. In this work, we study the performance of deadline-constrained bursty traffic with retransmissions providing a Markov chain-based analysis. The aim is to reveal the trade-off between the packet deadline and the number of retransmissions as a function of the arrival rate, and pave the way towards finding the optimal number of retransmissions, given the packet deadline and packet arrival rate. Furthermore, performance evaluation is conducted for a user with varying transmit probability and different number of retransmissions. The results reveal the effect of these parameters on the drop probability and average throughput showing the values under which, improved performance can be obtained.