Embedded memories account for a large fraction of the overall silicon area and power consumption in modern SoC(s). While embedded memories are typically realized with SRAM, alternative solutions, such as embedded dynamic memories (eDRAM), can provide higher density and/or reduced power consumption. One major challenge that impedes the widespread adoption of eDRAM is that they require frequent refreshes potentially reducing the availability of the memory in periods of high activity and also consuming significant amount of power due to such frequent refreshes. Reducing the refresh rate while on one hand can reduce the power overhead, if not performed in a timely manner, can cause some cells to lose their content potentially resulting in memory errors. In this paper, we consider extending the refresh period of gain-cell based dynamic memories beyond the worst-case point of failure, assuming that the resulting errors can be tolerated when the use-cases are in the domain of inherently error-resilient applications. For example, we observe that for various data mining applications, a large number of memory failures can be accepted with tolerable imprecision in output quality. In particular, our results indicate that by allowing as many as 177 errors in a 16 kB memory, the maximum loss in output quality is 11%. We use this failure limit to study the impact of relaxing reliability constraints on memory availability and retention power for different technologies.