Will I still receive my monthly payout if I can't access Brave?
If your device is lost, damaged, corrupted, reset, or anything else that causes you to permanently lose access to that install of Brave you should still receive your monthly payout if Brave was connected to a partner exchange at the time you stopped being able to access it.
If you are knowingly going to lose access to Brave (resetting/reinstalling your device etc.) it is best if you take a screenshot of the General Info tab of brave://rewards-internals
just in case something goes wrong and you need to contact support for help. Don't share this screenshot with anyone who you cannot verify is a member of Brave's staff - the info shown on the screenshot should be treated like you would treat the seed phrase for any crypto wallet, or any password to a banking website.
If your device was not connected to a partner exchange then you will not receive your monthly payout, and have lost any BAT that was previously paid out.
Be aware this may have changed recently, as the claim process sometimes requires manual actions from the user. [Current May 4 2022]