@shetlerbones the above questions were asked for a reason. Things like which version of Brave you’re using is quite important.
Have you made sure to check your Shields settings? For example, do you have it set to block cookies on Google?
What about your settings at brave://settings/clearBrowserData for the On Exit portion, do you have anything selected?
How about the option to clear all cookies and site data when you close all windows, which is at brave://settings/cookies?
Are you using any extensions? If so, try to disable or remove them and see if it still does it.