• Setup a project with a few assets
• Ensure you have an index in your Asset folder (not the default index in UserSettings).
• Open the search window. Validate that you can search assets in your project.
• Close the search window.
• Close Unity.
• Reopen Unity.
• Open the search window. See that the Progress bar for indexing restarts. Alternatively you can look at <Project>\Library\Search and see that the index file are deleted when you start Unity.

Woararound: if you only have an index file in UserSettings this won't happen.