Updating the OS should never affect an installed application. Make sure you are actually installing the application properly. When done correctly, the Brave app will live in the Applications folder.
1• Download the app from the Brave.com website. This will deposit the disk image Brave-Browser.dmg into your Downloads folder (or wherever you have directed your downloads to go).
2• Double-click Brave-Browser.dmg and the disk will appear on your Desktop along with its Finder window instructing you to drag the Brave app onto the Applications folder icon there to copy the app into your Applications folder.
3• Eject the Brave browser disk icon from the Desktop.
4• You can now use Launchpad to launch the Brave app. Then control-click the Brave icon in the Dock and select Options > Keep in Dock to have it remain always available in the Dock.
To reclaim the 230 MB of drive space used by the Brave download, you can simply delete Brave-Browser.dmg from your Downloads folder. If you ever need to reinstall the app, just get a fresh download from the web.
FYI, the steps above are typical of most apps downloaded directly from their developers' websites.