From the strength of the factorization problem to back it RSA remains to be one of the most powerful algorithm under public key cryptosystem. The main feature of the algorithm is that the key length can be variable. RSA algorithm is an encryption algorithm which is still used in the industry for various applications. This paper discusses on the nature of RSA algorithm when repeated encryption is done on it. It also focuses on the situation when on small repeated encryption RSA gives back the original plaintext what may be the possible cause.