KopiLuwak,
To be a little more clear, I used the Brave search URL address:
in the same fashion as going to the DuckDuckGo search engine.
I selected a Brave search result among the listed results (for my search criteria), and then, I followed the progress of that [specific search result] webpage being displayed . . . by testing an immediate return (back button) to the listed results - they were still intact.
So, you are probably placing your search criteria in the Brave browser URL address field . . . and that bit of info may help Brave support.