Sheep milk from local breeds is important for the production of high-quality cheeses throughout the Mediterranean region, such as Manchego cheese in Spain. To maintain sustainable and efficient production, it is necessary to reach a better understanding of how the composition and hygiene of the milk affect the coagulation process, with the aim of optimizing production yield. This study implemented a stochastic production frontier function to estimate the potential production of curd and efficiency using data from the four seasons of a study of 77 Manchega sheep farms. The Cobb–Douglas production frontier model was estimated using the maximum likelihood estimation method. The results showed that the content of protein, lactose, and fat exhibited increasing returns to scale, with protein content being the most significant factor for curd production. Approximately half of the inefficiency was due to factors related to the technological properties and the hygiene of the milk. The pH, curd firmness, and concentration of lactic acid bacteria improved the efficiency of coagulation, while the concentration of spores of lactate-fermenting Clostridium spp., Pseudomonas spp., staphylococci, and catalase-negative gram-positive cocci favored the inefficiency of the coagulation process. To date, this is the first study to evaluate the effect of different factors, such as microbial groups, milk composition, and technological properties, on the efficiency of the coagulation process in dairy sheep.