A fundamental question in leakage-resilient cryptography is: can leakage resilience always be amplified by parallel repetition? It is natural to expect that if we have a leakage-resilient primitive tolerating $ell$ bits of leakage, we can take $n$ copies of it to form a system tolerating $nell$ bits of leakage. In this paper, we show that this is not always true. We construct a public key encryption system which is secure when at most $ell$ bits are leaked, but $n$ copies of the system are insecure when $nell$ bits are leaked. Our results hold either in composite order bilinear groups under a variant of the subgroup decision assumption emph{or} in prime order bilinear groups under the decisional linear assumption where the public key systems share a common reference parameter.