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Robust beamforming methods are studied to support relay-assisted coordinated multi-point (CoMP) retransmissions in downlink multi-cell networks. Linear beamformers (BFers) for relay stations of different cells are jointly designed to maintain, in a CoMP amplify-and-forward (AF) relaying manner, the target signal to interference-plus-noise ratios (SINR) at the cellular boundaries of this type of networks. Considering the feasibility in realizations and deployments, BFer designs are only allowed to use the channel state information (CSI) feedbacks of the wireless links inside a network. This kind of designs turns out to be a challenging optimization problem when attempting to maintain the SINR under the estimation and quantization errors in CSI. A conservative criterion and solution method is proposed for this robust design problem. Despite the conservativeness, the proposed method appears to provide an effective BFer design for CoMP AF relaying, either from the perspective of power consumption or from the viewpoints of BFers' complexity and feasibility in syntheses. Simulations also show that when applying the proposed CoMP AF relaying method in Automatic Retransmission reQuest (ARQ), data throughput can be efficiently increased for users close to the joint cellular boundaries inside a multi-cell network.