Artificial intelligence and machine learning (AI/ML) models have been adopted in a wide range of healthcare applications, from medical image computing and analysis to continuous health monitoring and management. Recent data have demonstrated a clear trend that AI/ML model sizes, as well as their computational complexity, memory consumption and the scale of the required training data and costs, are experiencing an exponential increase. The developments in current computing hardware platforms, storage infrastructure, networking and domain expertise cannot keep up with this exponential growth in resources demanded by the AI/ML models. Here, we first analyse this recent trend and highlight that there are resource sustainability issues in AI/ML for healthcare. We then present various algorithm/system innovations that will help address these issues. We finally outline future directions to proactively and prospectively tackle these resource sustainability issues.