The sensitivity of the agricultural production system to short- and long-term climate variations significantly affects the availability and prices of food resources, raising relevant issues of sustainability and food security. Globally, productive systems have adapted to climate change, leading to increased yields over the past century. However, the extent to which these adaptations mitigate the impacts of short-term climate fluctuations, both extreme and ordinary, remains poorly studied. To evaluate the vulnerability of crop yield to short-term climate fluctuations and to determine whether it changes over time, we conducted a statistical analysis focusing on one of the main crops in the Abruzzo region (central Italy) as a case study: grape. The study involves correlation analysis between opportune climatic indices (SPI and SPEI) and grape yield data over the sixty-year period from 1952 to 2014, aimed at evaluating the impact of short-term climatic fluctuations—both extreme and ordinary—on crop yield. Our findings reveal an increasing correlation, mainly in the summer–autumn season, which suggests a rising sensitivity of the productive system over time. The observed increase is indicative of the Abruzzo grape production system’s adaptation to climate change, resulting in higher overall yields but not enhancing the response to short-term climatic fluctuations.