Under brave://flags there is a “Tab Groups Save” that I have enabled and was testing out. Once enabled I have the option to right click a group and turn on a slider for “Save Group”. The only problem is that when I close the browser and open it up again, these saves are turned off and are not showing on the toolbar.
This isn’t causing an immediate issue as I still keep my tabs in groups nad I ensure it is the last window I close so that they continue where I left off. It would be great if the save group function worked so I didn’t have to use the “continue where I left off” function as I like to have multiple windows.
My current work around is to use 3 browsers to achieve multiple windows so I don’t forget to close Brave window last.
I have reviewed other similar topics, but none cover this specific issue.
Here are the tab groups saved:
Here are tab groups after relaunch of browser:
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Just stumbled across this post and enabled this feature. Appears to be working in Release v1.49.120. Closed the browser and reopened and still there! Looks like this may have been posted at v1.45.x, so is definitely saving in the newest release.
Love, love, love this feature. I can actually see the names on open tabs now! Hopefully this will be a permanent thing.
My 'just in case" workaround: I bookmark the tabs in my groups in separate bookmark folders labeled with the name of the group just in case the experiment goes awry. 
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When I click the save toggle, my brave just crashes.
What is the purpose of that feature?
I think its important to remember here that these flags are (typically) not implemented by us. 99% of them are implemented in the Chromium engine and we simply inherit them. Additionally, by nature, these flags are experimental and very well may contain bugs or introduce new issues.