In 2006, Chatterjee and Sarkar proposed a hierarchical identity-based encryption (HIBE) scheme which can support an unbounded number of identity levels. This property is particularly useful in providing forward secrecy by embedding time components within hierarchical identities. In this paper we show that their scheme does not provide the claimed property. Our analysis shows that if the number of identity levels becomes larger than the value of a fixed public parameter, an unintended receiver can reconstruct a new valid ciphertext and decrypt the ciphertext using his or her own private key. The analysis is similarly applied to a multi-receiver identity-based encryption scheme presented as an application of Chatterjee and Sarkar's HIBE scheme.