This study presents a fabrication process for lithium-drifted silicon (Si(Li)) detectors that, compared to previous methods, allows for mass production at a higher yield, while providing a large sensitive area and low leakage currents at relatively high temperatures. This design, developed for the unique requirements of the General Antiparticle Spectrometer (GAPS) experiment, has an overall diameter of 10 cm, with ~9 cm of active area segmented into 8 readout strips, and an overall thickness of 2.5 mm, with $gtrsim$2.2 mm ($gtrsim$90%) sensitive thickness. An energy resolution $lesssim$4 keV full-width at half-maximum (FWHM) for 20-100 keV X-rays is required at the operating temperature ~-40C, which is far above the liquid nitrogen temperatures conventionally used to achieve fine energy resolution. High-yield production is also required for GAPS, which consists of $gtrsim$1000 detectors. Our specially-developed Si crystal and custom methods of Li evaporation, diffusion and drifting allow for a thick, large-area and uniform sensitive layer. We find that retaining a thin undrifted layer on the p-side of the detector drastically reduces the leakage current, which is a dominant component of the energy resolution at these temperatures. A guard-ring structure and optimal etching of the detector surface are also confirmed to suppress the leakage current. We report on the mass production of these detectors that is ongoing now, and demonstrate it is capable of delivering a high yield of ~90%.