To help us diagnose the problem, we need a bit more information:
- More Detailed Scenario - Please describe exactly what type of search or which part of the workbench you're using when the issue occurs? The search function appears in multiple places, so a precise description will help.
- Browser Console - Are there any errors or warnings in the Firefox console when the delay happens?
- Setup Details - You've mentioned that you're using GraphDB version 10.8.4 on a self-hosted server. Can you confirm if you're using the free version or a licensed one?
- Data Characteristics - It would also be useful to know the approximate volume and nature of the data in your database.
With these details, we can better investigate your problem.

Best regards,
Stilyana