Two types of packet transmission schemes are prevalent in duty-cycled wireless sensor networks, i.e., single packet transmission and aggregated packet transmission which integrates multiple packets in one frame. While most existing models are developed based on an error-free channel assumption, this paper evaluates the performance of both transmission schemes under error-prone channel conditions. We develop a four-dimensional discrete-time Markov chain model to investigate the impact of channel impairments on the performance of frame transmissions. Together with tracking the number of packets in the queue, number of retransmissions and number of active nodes, the fourth dimension of the model is able to capture the channel behavior at the frame-level. Based on the developed model, we analyze packet loss probability, packet delay, throughput, node energy consumption, and energy efficiency under various channel conditions. To further reduce energy consumption, we propose an event-triggered sleeping (ETS) energy mode for synchronous duty-cycling medium access control protocols. Numerical results reveal to which extent channel impairments may deteriorate the network performance, as well as the advantage of adopting aggregated packet transmission. The benefit brought by the ETS energy mode is also demonstrated showing that the network lifetime is considerably extended, particularly in low traffic load scenarios.