Our analysis of recent AI4H publications reveals that, despite a trend toward utilizing open datasets and sharing modeling code, 74% of AI4H papers still rely on private datasets or do not share their code. This is especially concerning in healthcare applications, where trust is essential. Furthermore, inconsistent and poorly documented data preprocessing pipelines result in variable model performance reports, even for identical tasks and datasets, making it challenging to evaluate the true effectiveness of AI models. Despite the challenges posed by the reproducibility crisis, addressing these issues through open practices offers substantial benefits. For instance, while the reproducibility mandate adds extra effort to research and publication, it significantly enhances the impact of the work. Our analysis shows that papers that used both public datasets and shared code received, on average, 110% more citations than those that do neither--more than doubling the citation count. Given the clear benefits of enhancing reproducibility, it is imperative for the AI4H community to take concrete steps to overcome existing barriers. The community should promote open science practices, establish standardized guidelines for data preprocessing, and develop robust benchmarks. Tackling these challenges through open-source development can improve reproducibility, which is essential for ensuring that AI models are safe, effective, and beneficial for patient care. This approach will help build more trustworthy AI systems that can be integrated into healthcare settings, ultimately contributing to better patient outcomes and advancing the field of medicine.