Accessing research data at any time is what FAIR (Findable Accessible Interoperable Reusable) data sharing aims to achieve at scale. Yet, we argue that it is not sustainable to keep accumulating and maintaining all datasets for rapid access, considering the monetary and ecological cost of maintaining repositories. Here, we address the issue of cold data storage: when to dispose of data for offline storage, how can this be done while maintaining FAIR principles and who should be responsible for cold archiving and long-term preservation.