Cellular memory is a ubiquitous phenomenon in cell biology. Using numerical simulation and theoretical analysis, we explored the robustness of cellular memory to intrinsic noise in a transcriptional positive feedback system. Without noise, the system could create two stable steady states and function as a memory module. Memory robustness index and mean first-passage time were used to quantify the robustness of memory. Large cell size and strong cooperativity in binding enhanced memory storage remarkably. Adding a second positive feedback loop improved persistent memory significantly, whereas including a negative one destabilized memory storage. These are consistent with experimental observations. We interpret why positive feedback loops are actively involved in epigenetic memory from a dynamical systems perspective.