The FBI’s background-check system is missing millions of records of criminal convictions, mental illness diagnoses and other flags that would keep guns out of potentially dangerous hands, a gap that contributed to the shooting deaths of 26 people in a Texas church this week.

Experts who study the data say government agencies responsible for maintaining such records have long failed to forward them into federal databases used for gun background checks — systemic breakdowns that have lingered for decades as officials decided they were too costly and time-consuming to fix.