At 714, the enclave entry epoch variable associated with the RLP and one or more enclave reference counters associated with the RLP are adjusted to simulate the RLP re-entering the enclave mode as if an asynchronous exit operation had been performed by the RLP and an instruction to re-enter the enclave mode (e.g., ERESUME instruction) was subsequently executed. More specifically, the enclave entry epoch variable associated with the RLP is adjusted to equal the current value of the global epoch variable. In addition, the enclave reference counters are adjusted as if the RLP just re-entered the enclave mode. For example, the enclave reference counter for the current epoch is incremented by 1, and the enclave reference counter for the prior epoch is decremented by 1. This enables the RLP to continue running in the enclave mode when an enclave page is evicted, thus avoiding the excessive clock cycles that would otherwise be consumed by performing an asynchronous exit from the enclave mode and a subsequent re-entry into the enclave mode.