Memristive Crossbar Arrays (MCAs) are widely used in designing fast and compact neuromorphic systems. However, such systems require on-chip implementation of the backpropagation algorithm to accommodate process variations. This paper proposes a low hardware overhead on-chip implementation of the backpropagation algorithm that utilizes effectively the very dense MCAs. On-chip learning using the proposed architecture increases the reliability of the neuromorphic system in the presence of process variations in the neural component. The second contribution of this paper is an architectural enhancement to cope with another reliability consideration, namely the aging transistors in the MCA. Experimental results show the impact of reliability enhancement.