This study examines vulnerabilities in transformer-based automated short-answer grading systems used in medical education, with a focus on how these systems can be manipulated through adversarial gaming strategies. Our research identifies three main types of gaming strategies that exploit the system's weaknesses, potentially leading to false positives. To counteract these vulnerabilities, we implement several adversarial training methods designed to enhance the systems' robustness. Our results indicate that these methods significantly reduce the susceptibility of grading systems to such manipulations, especially when combined with ensemble techniques like majority voting and ridge regression, which further improve the system's defense against sophisticated adversarial inputs. Additionally, employing large language models such as GPT-4 with varied prompting techniques has shown promise in recognizing and scoring gaming strategies effectively. The findings underscore the importance of continuous improvements in AI-driven educational tools to ensure their reliability and fairness in high-stakes settings.