To elucidate principles operating in native biological systems and to develop novel biotechnologies, synthetic biology aims to build and integrate synthetic gene circuits within native transcriptional networks. The utility of synthetic gene circuits for cell engineering relies on the ability to control the expression of all constituent transgene components. Transgene silencing, defined as the loss of expression over time, persists as an obstacle for engineering primary cells and stem cells with transgenic cargos. In this review, we highlight the challenge that transgene silencing poses to the robust engineering of mammalian cells, outline potential molecular mechanisms of silencing, and present approaches for preventing transgene silencing. We conclude with a perspective identifying future research directions for improving the performance of synthetic gene circuits.