The "Brave browser Xwindow" automatically closes after using the application for a few minutes.
That is for your own protection to prevent being served ads.
Just kidding, welcome to the forum @Phoenix.
Well, I recently read that @anon56724355 had similar problem with Brave, so he switched to brave-bin which solved the issue for him.
You should give it a shot.
The setup assistant also installs the -bin version now