In this paper, we evaluate by computer simulations the signal energy per information bit (Eb/N0) for rate compatible punctured turbo (RCPT) coded hybrid ARQ for direct sequence code division multiple access (DS-CDMA) with antenna diversity reception and Rake combining in a frequency selective Rayleigh fading channel when the number of allowable retransmissions is limited. When the number of allowable retransmissions is unlimited, transmitting minimum amount of redundancy bits with each retransmission would result in the highest throughput as unnecessary redundancy is avoided. However in a practical system, the number of retransmissions allowed is limited to avoid unacceptable time delay before the successful transmission of a packet. When the number of retransmissions is limited, residual bit error is produced. In this paper, we consider different RCPT Hybrid ARQ schemes with limited number of retransmissions. It is found that the type II hybrid ARQ scheme is the most favorable in terms of required Eb/N0 for a given bit error rate (BER), while the type I hybrid ARQ scheme, is the most favorable for delay sensitive systems. For the type II hybrid ARQ schemes, the minimum required Eb/N0 is attained after all the parity bits are transmitted and hence depends on the puncturing period.