Kevin:
1. Are the locators that are disappearing on you created with the Create Address Locator tool or the Create Locator tool?
2. What version of ArcGIS Pro did you encounter this behavior?
3. Does the locator that is rebuilt not show in the Catalog pane under the Locators folder and in the Locate pane in the Provider Settings?
Are you using the Rebuild Address Locator tool to rebuild the locator? If so, do you remove the locator from the project before running the tool?
-Shana