In DBSec’11, Li et al. showed that Kim and Chung’s password-based remote user authentication scheme is vulnerable to various attacks if the smart card is non-tamper resistant. Consequently, an improved version was proposed and claimed that it is secure against smart card security breach attacks. In this paper, however, we will show that Li et al.’s scheme still cannot withstand offline password guessing attack under the non-tamper resistance assumption of the smart card. In addition, their scheme is also prone to denial of service attack and fails to provide user anonymity and forward secrecy. Therefore, a robust scheme with a brief analysis is presented to overcome the identified drawbacks.