This has only been a problem in the past week or so, I’ve been using Brave for many years and have not had this problem until recently. I don’t have it set to delete anything on closing, it’s just doing it on its own.
There is a lot of info to study. Within it, you may determine IF there is a chance for your recovering your passwords.
MUCH depends upon whether or not you have been maintaining routine data backups -AND- your willingness to study.
Studying the recent information available:
Searching for keyword passwords in the topic/title of issues, here at the Brave Community:
‘https://community.brave.app/search?q=passwords%20in%3Atitle%20order%3Alatest’
Yes I have a backup of all of my passwords in a CSV file. I have to import those passwords every time I reboot my PC and the browser logs me out of all websites despite keeping my cookies.
Thankfully, you have not lost your passwords.
The unfortunately hard lesson: Computing device users CANNOT rely upon any single Password Manager.
I learned that, 56 years ago. Including the requirement: User data must be backed up, at least twice and to at least 2 different locations that are not on the computing device.
That is my editorial comment here, for anybody who drops by, looking for answers.
Again, thank you for making the effort to back up your data.
Having the data is nice I agree, but I want the browser to keep the passwords stored in the app like it is supposed to do and had previously done for nearly 5 years of use; I want a solution for the problem. 
It also logs me out of all websites on PC reboot, which is the bigger and more frustrating problem that I want a solution for.
The study that I suggest in a previous reply, will help you to see Brave’s situation.
My own solution re that situation, has been to use a 3rd party password manager ← that I adopted long ago.
My military boot camp instructor tips re determination to remain logged in - but not a guarantee:
Yes I do all of that already (except for not letting letting my PC go to sleep mode/turn off, that’s completely unfeasible), those settings are not the problem as they are unchanged from before I had this problem. “Simply back up the data” is not a solution to my problem.