In this paper, we propose to optimize the distribution of the average relay energy in a Cooperative Automatic Repeat reQuest (C-ARQ) scheme. We consider wireless transmissions over Rayleigh fading channels between two sources nodes, one relay node and one destination node. We propose to use specific relay and destination treatment for different possible cases. When only one received packet is detected erroneous, the relay retransmits it and the detection is based on the Maximum Ratio Combining (MRC). When both received packets are detected erroneous, the relay retransmits the combination of both packets and the Minimum Mean Square Error (MMSE) is used for packets detection. We propose to allocate to the relay different energies according to the number of retransmitted packets and also according to the retransmission number. Thus, we find the optimal relay energy distribution which maximizes the system throughput under constraints on the maximum transmitted energies. To do this, we derive semi-analytical bounds of the throughput and the average relay energy. Numerical results show that the relay energy optimization leads to a significant improvement compared to the fixed allocation relay energy scheme.