To support machine-type communication (MTC), massive multiple-input multiple-output (MIMO) has been considered for grant-free random access. In general, the performance of grant-free random access with massive MIMO is limited by the number of preambles and the number of active devices. In particular, when there are a number of active devices transmitting data packets simultaneously, the signal-to-interference-plus-noise ratio (SINR) cannot be high enough for successful decoding. In this paper, in order to improve performance, we consider immediate re-transmissions for an active device that has a low SINR although it does not experience preamble collision to exploit re-transmission diversity (RTD) gain. To see the performance of the proposed approach, we perform throughput analysis with certain approximations and assumption. Since the proposed approach can be unstable due to immediate re-transmissions, conditions for stable systems are also studied. Simulations are carried out and it is shown that analysis results reasonably match simulation results.