There is something disturbing in the ‘Brave-Browser’ folder located inside the ‘Library -> Application Support -> BraveSoftware’. If you put it on your desktop (don’t throw it away) Brave will no longer closes. You can recover the bookmarks file located in the folder ‘Brave-Browser -> Default’.
Of course you will have to adjust your preferences and settings again and also download the extensions again (Hoping that the problem isn’t caused by one of these).
I hope it can help you.