A gain-cell embedded DRAM (GC-eDRAM) is an attractive logic-compatible alternative to the conventional static random access memory (SRAM) for the implementation of embedded memories, as it offers higher density, lower leakage, and two-ported operation. However, it requires periodic refresh cycles to maintain its data which deteriorates due to leakage. The refresh-rate, which is traditionally set according to the worst cell in the array under extreme operating conditions, leads to a significant refresh power consumption and decreased memory availability. In this paper, we propose to reduce the cost of GC-eDRAM refresh by employing failure detection to lower the refresh-rate. A 4T dynamic complementary dual-modular redundancy bitcell is proposed to offer per-bit error detection, resulting in a substantial decrease in the refresh-rate and over 60% power reduction compared with the SRAM. The proposed approach is also compared with the conventional SRAM and GCeDRAM implementations with integrated error correction codes, demonstrating significant area and latency reductions.